arXiv math.LO Logic @mathLOb profile

arXiv math.LO Logic

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arXiv math.LO Logic

@mathLOb

2 years

Egbert Rijke: Introduction to Homotopy Type Theory

Introduction to Homotopy Type Theory

This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definitions and...

arxiv.org

1

32

118

arXiv math.LO Logic

@mathLOb

10 months

Toshiyasu Arai: An ordinal analysis of $\Pi_{N}$-Collection

An ordinal analysis of $Π_{N}$-Collection

In this paper we give an ordinal analysis of a set theory with $Π_{N}$-Collection.

arxiv.org

1

46

109

arXiv math.LO Logic

@mathLOb

4 years

Adonai S. Sant'Anna, Otavio Bueno, Marcio P. P. de França, Renato Brodzinski: Flow: the Axiom of Choice is independent from the Partition Principle

0

21

65

arXiv math.LO Logic

@mathLOb

3 years

Thorsten Altenkirch: Should Type Theory replace Set Theory as the Foundation of Mathematics

Should Type Theory replace Set Theory as the Foundation of Mathematics

We discuss why Type Theory is preferable as foundation of Mathematics compared to set theory.

arxiv.org

1

18

61

arXiv math.LO Logic

@mathLOb

3 years

Joel David Hamkins: Infinite Wordle and the Mastermind numbers

Infinite Wordle and the Mastermind numbers

I consider the natural infinitary variations of the games Wordle and Mastermind, as well as their game-theoretic variations Absurdle and Madstermind, considering these games with infinitely long...

arxiv.org

1

22

52

arXiv math.LO Logic

@mathLOb

4 years

Saul A. Kripke: The Collapse of the Hilbert Program: A Variation on the G\"odelian Theme

The Collapse of the Hilbert Program: A Variation on the Gödelian Theme

The Hilbert program was actually a specific approach for proving consistency. Quantifiers were supposed to be replaced by $ε$-terms. $ε{x}A(x)$ was supposed to denote a witness to...

arxiv.org

2

17

44

arXiv math.LO Logic

@mathLOb

6 months

Richard Zach: Logic in Mathematics and Computer Science

Logic in Mathematics and Computer Science

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics:...

arxiv.org

0

12

43

arXiv math.LO Logic

@mathLOb

11 months

Taishi Kurahashi, Rihito Takase: The Modal Logic of Provability and Forcing

The Modal Logic of Provability and Forcing

Solovay's arithmetical completeness theorem states that the modal logic of provability coincides with the modal logic $\mathbf{GL}$. Hamkins and Löwe studied the modal logical aspects of set...

arxiv.org

1

10

42

arXiv math.LO Logic

@mathLOb

10 months

Toshimichi Usuba: A note on \L o\'s's Theorem without the Axiom of Choice

A note on Łoś's Theorem without the Axiom of Choice

We study some topics about Łoś's theorem without assuming the Axiom of Choice. We prove that Łoś's fundamental theorem of ultraproducts is equivalent to a weak form that every ultrapower...

arxiv.org

0

17

39

arXiv math.LO Logic

@mathLOb

3 months

Joel David Hamkins, Theodor Nenu: Did Turing prove the undecidability of the halting problem?

Did Turing prove the undecidability of the halting problem?

We discuss the accuracy of the attribution commonly given to Turing's 1936 paper "On computable numbers..." for the computable undecidability of the halting problem, coming eventually to a nuanced...

arxiv.org

1

4

39

arXiv math.LO Logic

@mathLOb

1 year

Toshiyasu Arai: Lectures on Ordinal Analysis

Lectures on Ordinal Analysis

This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.

arxiv.org

1

18

38

arXiv math.LO Logic

@mathLOb

6 months

Henry Towsner: Proofs that Modify Proofs

Proofs that Modify Proofs

In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a...

arxiv.org

0

11

37

arXiv math.LO Logic

@mathLOb

2 years

Bokai Yao: Set Theory with Urelements

Set Theory with Urelements

This dissertation aims to provide a comprehensive account of set theory with urelements. In Chapter 1, I present mathematical and philosophical motivations for studying urelement set theory and...

arxiv.org

1

10

37

arXiv math.LO Logic

@mathLOb

9 months

Hanul Jeon: The proof-theoretic strength of Constructive Second-order set theories

The proof-theoretic strength of Constructive Second-order set theories

In this paper, we define constructive analogues of second-order set theories, which we will call $\mathsf{IGB}$, $\mathsf{CGB}$, $\mathsf{IKM}$, and $\mathsf{CKM}$. Each of them can be viewed as...

arxiv.org

1

11

34

arXiv math.LO Logic

@mathLOb

18 days

Henry Towsner, James Walsh: A classification of incompleteness statements

0

10

31

arXiv math.LO Logic

@mathLOb

4 years

Hisashi Aratake: Sheaves of Structures, Heyting-Valued Structures, and a Generalization of {\L}o\'s's Theorem

Sheaves of Structures, Heyting-Valued Structures, and a...

Sheaves of structures are useful to give constructions in universal algebra and model theory. We can describe their logical behavior in terms of Heyting-valued structures. In this paper, we first...

arxiv.org

1

13

31

arXiv math.LO Logic

@mathLOb

10 months

J. Julian Pulgarín, Andrés F. Uribe-Zapata: Which came first, set theory or logic?

Which came first, set theory or logic?

The construction of first-order logic and set theory gives rise to apparent circularities of mutual dependence, making it unclear which can act as a self-contained starting point in the foundation...

arxiv.org

0

4

29

arXiv math.LO Logic

@mathLOb

6 years

Klaas Pieter Hart : Machine learning and the Continuum Hypothesis

Machine learning and the Continuum Hypothesis

We comment on a recent paper that connects certain forms of machine learning to Set Theory. We point out that part of the set-theoretic machinery is related to a result of Kuratowski about...

arxiv.org

0

12

29

arXiv math.LO Logic

@mathLOb

2 years

Paolo Mancosu, Richard Zach: Some Unpublished Letters by G\"odel and von Neumann in the Fraenkel Archive

1

18

28

arXiv math.LO Logic

@mathLOb

2 years

Alec Rhea: An axiomatic approach to the multiverse of sets

An axiomatic approach to the multiverse of sets

Recent work in set theory indicates that there are many different notions of 'set', each captured by a different collection of axioms, as proposed by J. Hamkins in [Ham11]. In this paper we strive...

arxiv.org

1

9

29

arXiv math.LO Logic

@mathLOb

3 years

S. Awodey, N. Gambino, S. Hazratpour: Kripke-Joyal forcing for type theory and uniform fibrations

1

11

28

arXiv math.LO Logic

@mathLOb

3 months

Ali Enayat: Models of Set Theory: Extensions and Dead-ends

Models of Set Theory: Extensions and Dead-ends

This paper is a contribution to the study of extensions of arbitrary models of ZF (Zermelo-Fraenkel set theory), with no regard to countability or well-foundedness of the models involved. We...

arxiv.org

1

6

25

arXiv math.LO Logic

@mathLOb

4 years

Gianluca Paolini, Saharon Shelah: Torsion-Free Abelian Groups are Borel Complete

Torsion-Free Abelian Groups are Borel Complete

We prove that the Borel space of torsion-free Abelian groups with domain $ω$ is Borel complete, i.e., the isomorphism relation on this Borel space is as complicated as possible, as an...

arxiv.org

2

4

24

arXiv math.LO Logic

@mathLOb

3 years

Kameryn J. Williams: The $\omega$-th inner mantle

The $ω$-th inner mantle

This article investigates pathological behavior at the first limit stage in the sequence of inner mantles, obtained by iterating the definition of the mantle to get smaller and smaller inner...

arxiv.org

1

8

24

arXiv math.LO Logic

@mathLOb

19 days

Sam Sanders: Coding is hard

Coding is hard

A central topic in mathematical logic is the classification of theorems from mathematics in hierarchies according to their logical strength. Ideally, the place of a theorem in a hierarchy does not...

arxiv.org

0

7

22

arXiv math.LO Logic

@mathLOb

4 years

Joel David Hamkins, Russell Miller, Kameryn J. Williams : Forcing as a computational process

Forcing as a computational process

We investigate how set-theoretic forcing can be seen as a computational process on the models of set theory. Given an oracle for information about a model of set theory $\langle M,\in^M\rangle$,...

arxiv.org

0

4

21

arXiv math.LO Logic

@mathLOb

4 years

Saharon Shelah, Andrés Villaveces: Infinitary Logics and A.E.C

0

10

22

arXiv math.LO Logic

@mathLOb

3 years

Tatsuya Goto: Keisler's Theorem and Cardinal Invariants

Keisler's Theorem and Cardinal Invariants

We consider several variants of Keisler's isomorphism theorem. We separate these variants by showing implications between them and cardinal invariants hypotheses. We characterize saturation...

arxiv.org

1

7

21

arXiv math.LO Logic

@mathLOb

1 year

Daisuke Ikegami, Nam Trang: Preservation of AD via forcings

Preservation of AD via forcings

We show that assuming $\mathsf{ZF}+\mathsf{AD}^+ +$ "$V = \mathrm{L} \bigl(\wp (\mathbb{R})\bigr)$", any poset which increases $Θ$ does not preserve the truth of $\mathsf{AD}$. We also show...

arxiv.org

1

13

21

arXiv math.LO Logic

@mathLOb

2 years

Taichi Uemura: Normalization and coherence for $\infty$-type theories

1

10

22

arXiv math.LO Logic

@mathLOb

3 years

Matthew Foreman: Naive Descriptive Set Theory

Naive Descriptive Set Theory

The paper is a naive introduction to descriptive set theory. It is aimed mathematicians without a background in logic. The goal is to provide the basic facts used for applications of descriptive...

arxiv.org

1

10

21

arXiv math.LO Logic

@mathLOb

1 year

Bruce Blackadar, Ilijas Farah, Asaf Karagila: Hilbert Spaces Without Countable AC

Hilbert Spaces Without Countable AC

This article examines Hilbert spaces constructed from sets whose existence is incompatible with the Countable Axiom of Choice (CC). Our point of view is twofold: (1) We examine what can and cannot...

arxiv.org

1

14

21

arXiv math.LO Logic

@mathLOb

3 years

Will Boney, Stamatis Dimopoulos, Victoria Gitman, Menachem Magidor: Model Theoretic Characterizations of Large Cardinals Revisited

Model Theoretic Characterizations of Large Cardinals Revisited

In [Bon20], model theoretic characterizations of several established large cardinal notions were given. We continue this work, by establishing such characterizations for Woodin cardinals (and...

arxiv.org

1

8

21

arXiv math.LO Logic

@mathLOb

4 months

Hanul Jeon: The behavior of higher proof theory I: Case $\Sigma^1_2$

The behavior of higher proof theory I: Case $Σ^1_2$

The current ordinal analysis provides the proof-theoretic ordinal of a theory, which calibrates the robustness of the $Π^1_1$-consequences of the theory. We can ask whether there is an ordinal...

arxiv.org

1

3

20

arXiv math.LO Logic

@mathLOb

7 months

Juan Pablo Aguilera, Fedor Pakhomov: The Logic of Correct Models

The Logic of Correct Models

For each $n\in\mathbb{N}$, let $[n]ϕ$ mean "the sentence $ϕ$ is true in all $Σ_{n+1}$-correct transitive sets." Assuming Gödel's axiom $V = L$, we prove the following graded variant...

arxiv.org

0

4

20

arXiv math.LO Logic

@mathLOb

2 years

Richard Matthews, Michael Rathjen: Constructing the Constructible Universe Constructively

Constructing the Constructible Universe Constructively

We study the properties of the constructible universe, L, over intuitionistic theories. We give an extended set of fundamental operations which is sufficient to generate the universe over...

arxiv.org

2

5

19

arXiv math.LO Logic

@mathLOb

1 year

Anton Freund: An Introduction to Mathematical Logic

An Introduction to Mathematical Logic

This introduction begins with a section on fundamental notions of mathematical logic, including propositional logic, predicate or first-order logic, completeness, compactness, the...

arxiv.org

0

8

20

arXiv math.LO Logic

@mathLOb

9 months

Farmer Schlutzenberg: Low level definability above large cardinals

Low level definability above large cardinals

We study some connections between definability in generalized descriptive set theory and large cardinals, particularly measurable cardinals and limits thereof, working in ZFC. We show that if...

arxiv.org

0

5

18

arXiv math.LO Logic

@mathLOb

2 years

Rahim Moosa: Six lectures on model theory and differential-algebraic geometry

Six lectures on model theory and differential-algebraic geometry

This is a write-up of some lectures I gave in the Fall of 2021 at the Fields Institute in Toronto, as part of the Thematic Programme on Trends in Pure and Applied Model Theory. The goal of the...

arxiv.org

1

5

19

arXiv math.LO Logic

@mathLOb

9 months

Toshimichi Usuba: A note on uniform ultrafilters in a choiceless context

A note on uniform ultrafilters in a choiceless context

In \cite{HK}, Hayut and Karagila asked some questions about uniform ultrafilters in a choiceless context. We provide several answers to their questions.

arxiv.org

0

10

19

arXiv math.LO Logic

@mathLOb

1 year

Samuel Vargovčík: Well-Orderedness of the Bashicu Matrix System

Well-Orderedness of the Bashicu Matrix System

The Bashicu Matrix System is a recursive system of ordinal notations created by the user BashicuHyudora of the japanese Googology Wiki. In this paper, we prove that the Bashicu Matrix System is...

arxiv.org

1

7

17

arXiv math.LO Logic

@mathLOb

5 years

Pierre Pradic, Chad E. Brown : Cantor-Bernstein implies Excluded Middle

Cantor-Bernstein implies Excluded Middle

We prove in constructive logic that the statement of the Cantor-Bernstein theorem implies excluded middle. This establishes that the Cantor-Bernstein theorem can only be proven assuming the full...

arxiv.org

2

7

18

arXiv math.LO Logic

@mathLOb

4 years

Taras Banakh : Classical Set Theory: Theory of Sets and Classes

Classical Set Theory: Theory of Sets and Classes

This is a short introductory course to Set Theory, based on axioms of von Neumann--Bernays--Gödel (briefly NBG). The text can be used as a base for a lecture course in Foundations of...

arxiv.org

0

10

18

arXiv math.LO Logic

@mathLOb

3 years

Anton Freund: Unprovability in Mathematics: A First Course on Ordinal Analysis

1

6

17

arXiv math.LO Logic

@mathLOb

1 year

William H. Wheeler: Andrew Wiles' Proof of Fermat's Last Theorem, As Expected, Does Not Require a Large Cardinal Axiom. A Discussion of Colin McLarty's "The Large Structures of Grothendieck Founded on Finite-Order Arithme...

Andrew Wiles' Proof of Fermat's Last Theorem, As Expected,...

Andrew Wiles' proof of Fermat's Last Theorem, with an assist from Richard Taylor, focused renewed attention on the foundational question of whether the use of Grothendieck's Universes in number...

arxiv.org

0

6

18

arXiv math.LO Logic

@mathLOb

2 years

Anders Mörtberg, Max Zeuner: A Univalent Formalization of Affine Schemes

A Univalent Formalization of Constructive Affine Schemes

We present a formalization of constructive affine schemes in the Cubical Agda proof assistant. This development is not only fully constructive and predicative, it also makes crucial use of...

arxiv.org

1

8

17

arXiv math.LO Logic

@mathLOb

3 years

Grigor Sargsyan, Takehiko Gappo: On the derived models of self iterable universes

1

9

16

arXiv math.LO Logic

@mathLOb

8 months

Yudai Suzuki, Keita Yokoyama: On the $\Pi^1_2$ consequences of $\Pi^1_1$-$\mathsf{CA}_0$

On the $Π^1_2$ consequences of $Π^1_1$-$\mathsf{CA}_0$

The system $Π^1_1$-$\mathsf{CA}_0$ is known as the strongest system of the \textit{big five} in reverse mathematics. It is known that some theorems represented by a $Π^1_2$ sentence, for...

arxiv.org

0

4

17

arXiv math.LO Logic

@mathLOb

3 years

Valeria de Paiva, Samuel G. da Silva: Kolgomorov-Veloso Problems and Dialectica Categories

Kolmogorov-Veloso Problems and Dialectica Categories

We investigate the categorical connection between Dialectica constructions, Kolmogorov problems, Veloso problems and Blass problems. We show that the work of Kolmogorov can be regarded as a bridge...

arxiv.org

2

4

17

arXiv math.LO Logic

@mathLOb

5 months

Emi Je\v{r}\'abek: A note on the theory of well orders

A note on the theory of well orders

We give a simple proof that the first-order theory of well orders is axiomatized by transfinite induction, and that it is decidable.

arxiv.org

1

3

16

arXiv math.LO Logic

@mathLOb

9 months

Hanul Jeon, James Walsh: Generalized ordinal analysis and reflection principles in set theory

Generalized ordinal analysis and reflection principles in set theory

It is widely claimed that the natural axiom systems$\unicode{x2013}$including the large cardinal axioms$\unicode{x2013}$form a well-ordered hierarchy. Yet, as is well-known, it is possible to...

arxiv.org

0

3

15

arXiv math.LO Logic

@mathLOb

3 years

Kenta Tsukuura: Prikry-type forcing and the set of possible cofinalities

1

5

14

arXiv math.LO Logic

@mathLOb

5 months

Ralf Schindler, Taichi Yasuda: Martin's Maximum${}^{\ast, ++}_{\mathfrak{c}}$ in $\mathbb{P}_{\max}$ extensions of strong models of determinacy

Martin's Maximum${}^{\ast, ++}_{\mathfrak{c}}$ in...

We study a strengthening of $\mathrm{MM}^{++}$ which is called $\mathrm{MM}^{\ast, ++}$ and which was introduced by Asperó and Schindler. We force its bounded version $\mathrm{MM}^{\ast,...

arxiv.org

0

7

17

arXiv math.LO Logic

@mathLOb

5 months

Fedor Pakhomov, Michael Rathjen, Dino Rossegger: Feferman's completeness theorem

Feferman's completeness theorem

Feferman proved in 1962 that any arithmetical theorem is a consequence of a suitable transfinite iteration of full uniform reflection of $\mathsf{PA}$. This result is commonly known as Feferman's...

arxiv.org

0

6

16

arXiv math.LO Logic

@mathLOb

3 years

Grigor Sargsyan, Nam Trang, Trevor Wilson: Ideals and Strong Axioms of Determinacy

Ideals and Strong Axioms of Determinacy

We show that the following two theories are equiconsistent: (T) ZFC, CH and "There is a dense ideal on the first uncountable cardinal such that if j is the generic embedding associated with it...

arxiv.org

1

8

15

arXiv math.LO Logic

@mathLOb

9 months

Moti Gitik, Yair Hayut, Asaf Karagila: The first measurable can be the first inaccessible cardinal

The first measurable can be the first inaccessible cardinal

In [7] the second and third author showed that if the least inaccessible cardinal is the least measurable cardinal, then there is an inner model with $o(κ)\geq2$. In this paper we improve...

arxiv.org

0

6

16

arXiv math.LO Logic

@mathLOb

6 years

Richard Zach : Non-Analytic Tableaux for Chellas's Conditional Logic CK and Lewis's Logic of Counterfactuals VC

1

7

15

arXiv math.LO Logic

@mathLOb

2 years

Daisuke Ikegami, Philipp Schlicht: Forcing over choiceless models and generic absoluteness

Forcing over choiceless models and generic absoluteness

We develop a toolbox for forcing over arbitrary models of set theory without the axiom of choice. In particular, we introduce a variant of the countable chain condition and prove an iteration...

arxiv.org

1

8

16

arXiv math.LO Logic

@mathLOb

7 years

Albert Visser : From Tarski to Gödel. Or, how to derive the Second Incompleteness Theorem from the Undefinability of Truth without Self-reference

1

4

15

arXiv math.LO Logic

@mathLOb

3 years

Takayuki Kihara: Rethinking the notion of oracle: A link between synthetic descriptive set theory and effective topos theory

Rethinking the notion of oracle: A prequel to Lawvere-Tierney...

We present three different perspectives of oracle. First, an oracle is a blackbox; second, an oracle is a tool to change the way we access mathematical objects; and third, an oracle is a factor...

arxiv.org

1

9

15

arXiv math.LO Logic

@mathLOb

1 month

Amirhossein Akbar Tabatabai: An Introduction to Categorical Proof Theory

An Introduction to Categorical Proof Theory

These expanded lecture notes are based on a tutorial on categorical proof theory presented at the summer school associated with the conference "Topology, Algebra, and Categories in Logic...

arxiv.org

0

16

arXiv math.LO Logic

@mathLOb

5 years

Steve Awodey : Sheaf Representations and Duality in Logic

Sheaf Representations and Duality in Logic

The fundamental duality theories relating algebra and geometry that were discovered in the mid-20th century can also be applied to logic via its algebraization under categorical logic. They...

arxiv.org

0

6

15

arXiv math.LO Logic

@mathLOb

10 months

Assaf Rinot: May the successor of a singular cardinal be Jonsson?

May the successor of a singular cardinal be Jonsson?

In this survey, we collect necessary conditions for the successor of a singular cardinal to be Jonsson.

arxiv.org

0

4

15

arXiv math.LO Logic

@mathLOb

3 years

Henry Towsner, Rose Weisshaar, Linda Westrick: Borel combinatorics fail in HYP

Borel combinatorics fail in HYP

We characterize the completely determined Borel subsets of HYP as exactly the omega_1^{ck} subsets of HYP. As a result, HYP believes there is a Borel well-ordering of the reals, that the Borel...

arxiv.org

1

3

15

arXiv math.LO Logic

@mathLOb

2 years

Sam Sanders: Big in Reverse Mathematics: measure and category

Big in Reverse Mathematics: measure and category

The smooth development of large parts of mathematics hinges on the idea that some sets are `small' or `negligible' and can therefore be ignored for a given purpose. The perhaps most famous...

arxiv.org

1

4

14

arXiv math.LO Logic

@mathLOb

1 year

Koji Nuida: A Simple and Elementary Proof of Zorn's Lemma

A Simple and Elementary Proof of Zorn's Lemma

Zorn's Lemma is a well-known equivalent of the Axiom of Choice. It is usually regarded as a topic in axiomatic set theory, and its historically standard proof (from the Axiom of Choice) relies on...

arxiv.org

1

6

15

arXiv math.LO Logic

@mathLOb

3 years

Grigor Sargsyan, Nam Trang: The Largest Suslin Axiom

The Largest Suslin Axiom

We develop the basic fine structure theory of the minimal model of the Largest Suslin Axiom. In particular, we prove that that the minimal model of the Largest Suslin Axiom satisfies the Mouse Set...

arxiv.org

1

4

14

arXiv math.LO Logic

@mathLOb

2 years

Yinhe Peng, Guozhen Shen, Liuzhen Wu: A surjection from square onto power

A surjection from square onto power

It is shown that the existence of an infinite set $A$ such that $A^2$ maps onto $2^A$ is consistent with $\mathsf{ZF}$.

arxiv.org

1

2

13

arXiv math.LO Logic

@mathLOb

4 years

Joel David Hamkins, Wojciech Aleksander Wołoszyn: Modal model theory

1

9

15

arXiv math.LO Logic

@mathLOb

4 years

Monroe Eskew : Integration via ultrafilters

Integration with filters

We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic...

arxiv.org

0

8

15

arXiv math.LO Logic

@mathLOb

4 months

Miguel A. Cardona, Adam Marton, Jaroslav Supina: Cardinal characteristics associated with small subsets of reals

Cardinal characteristics associated with small subsets of reals

Inspired by Bartoszyński's work on small sets, we introduce a new ideal defined by interval partitions on natural numbers and summable sequences of positive reals. Similarly, we present another...

arxiv.org

1

4

12

arXiv math.LO Logic

@mathLOb

4 years

Joerg Brendle: Some Forcing Techniques: Ultrapowers, templates, and submodels

Modern Forcing Techniques related to Finite Support Iteration:...

This is an expository paper about several sophisticated forcing techniques closely related to standard finite support iterations of ccc partial orders. We focus on the four topics of ultrapowers...

arxiv.org

1

2

13

arXiv math.LO Logic

@mathLOb

10 months

Tom Benhamou, Natasha Dobrinen: On the Tukey types of Fubini products

On the Tukey types of Fubini products

We extend the class of ultrafilters $U$ over countable sets for which $U\cdot U\equiv_T U$, extending several results from \cite{Dobrinen/Todorcevic11}. In particular, we prove that for each...

arxiv.org

0

4

13

arXiv math.LO Logic

@mathLOb

4 years

Johanna N.Y. Franklin, Rupert Hölzl, Alexander Melnikov, Keng Meng Ng, Daniel Turetsky: Computable classifications of continuous, transducer, and regular functions

Computable classifications of continuous, transducer, and regular functions

We develop a systematic algorithmic framework that unites global and local classification problems using index sets. We prove that the classification problem for continuous (binary) regular...

arxiv.org

0

4

14

arXiv math.LO Logic

@mathLOb

5 years

Toshimichi Usuba : Choiceless Löwenheim-Skolem property and uniform definability of grounds

0

9

14

arXiv math.LO Logic

@mathLOb

4 years

Philip Welch: Characterisations of Variant Transfinite Computational Models: Infinite Time Turing, Ordinal Time Turing, and Blum-Shub-Smale machines

1

3

14

arXiv math.LO Logic

@mathLOb

4 years

Michael Rathjen: Well-Ordering Principles in Proof Theory and Reverse Mathematics

0

4

14

arXiv math.LO Logic

@mathLOb

4 years

Landon D. C. Elkind, Richard Zach: The Genealogy of $\lor$

The Genealogy of '$\lor$'

The use of the symbol $\lor$ for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol $\lor$ in its historical and logical context. Some...

arxiv.org

1

8

14

arXiv math.LO Logic

@mathLOb

27 days

Noah Schweber: Strong reducibilities and set theory

Strong reducibilities and set theory

We study Medvedev reducibility in the context of set theory -- specifically, forcing and large cardinal hypotheses. Answering a question of Hamkins and Li \cite{HaLi}, we show that the Medvedev...

arxiv.org

0

1

14

arXiv math.LO Logic

@mathLOb

4 years

Yinhe Peng, Liang Yu: TD implies CCR

TD implies CCR

Assuming $\mathrm{ZF}$, we prove that Turing determinacy ($\mathrm{TD}$) implies countable choice axiom for sets of reals ($\mathrm{CCR}$).

arxiv.org

1

14

arXiv math.LO Logic

@mathLOb

4 years

Joel David Hamkins, Hans Robin Solberg: Categorical large cardinals and the tension between categoricity and set-theoretic reflection

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5

13

arXiv math.LO Logic

@mathLOb

5 years

Toshiyasu Arai : Two remarks on proof theory of first-order arithmetic

Two remarks on proof theory of first-order arithmetic

In this note let us give two remarks on proof-theory of PA. First a derivability relation is introduced to bound witnesses for provable $Σ_{1}$-formulas in PA. Second Paris-Harrington's proof...

arxiv.org

0

4

13

arXiv math.LO Logic

@mathLOb

1 month

Sam Sanders: Connecting real and hyperarithmetical analysis

Connecting real and hyperarithmetical analysis

Going back to Kreisel in the Sixties, hyperarithmetical analysis is a cluster of logical systems just beyond arithmetical comprehension. Only recently natural examples of theorems from the...

arxiv.org

0

2

14

arXiv math.LO Logic

@mathLOb

7 months

Morenikeji Neri, Nicholas Pischke: Proof mining and probability theory

Proof mining and probability theory

We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie...

arxiv.org

0

1

14

arXiv math.LO Logic

@mathLOb

2 years

Tatsuya Goto: The comparability numbers and the incomparability numbers

The comparability numbers and the incomparability numbers

We introduce new cardinal invariants of a poset, called the comparability number and the incomparability number. We determine their value for well-known posets, such as $ω^ω$,...

arxiv.org

1

4

14

arXiv math.LO Logic

@mathLOb

3 years

Asaf Karagila, Noah Schweber: Choiceless Chain Conditions

1

8

14

arXiv math.LO Logic

@mathLOb

1 year

Richard Matthews: A Guide to Krivine Realizability for Set Theory

A Guide to Krivine Realizability for Set Theory

The method of realizability was first developed by Kleene and is seen as a way to extract computational content from mathematical proofs. Traditionally, these models only satisfy intuitionistic...

arxiv.org

0

5

14

arXiv math.LO Logic

@mathLOb

7 months

Takashi Yamazoe: Notes on the coexistence of limit notions

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4

14

arXiv math.LO Logic

@mathLOb

1 year

Lingyuan Ye: Categorical Structure in Theory of Arithmetic

Categorical Structure in Theory of Arithmetic

In this paper, we provide a categorical analysis of the arithmetic theory $IΣ_1$. We will provide a categorical proof of the classical result that the provably total recursive functions in...

arxiv.org

1

5

14

arXiv math.LO Logic

@mathLOb

10 months

Chris Lambie-Hanson, Dávid Uhrik: Hajnal--M\'{a}t\'{e} graphs, Cohen reals, and disjoint type guessing

Hajnal--Máté graphs, Cohen reals, and disjoint type guessing

A Hajnal--Máté graph is an uncountably chromatic graph on $ω_1$ satisfying a certain natural sparseness condition. We investigate Hajnal-Máté graphs and generalizations...

arxiv.org

0

2

14

arXiv math.LO Logic

@mathLOb

3 months

James Walsh: Modal definability in Kripke's theory of truth

Modal definability in Kripke's theory of truth

In Outline of a Theory of Truth, Kripke introduces some of the central concepts of the logical study of truth and paradox. He informally defines some of these -- such as groundedness and...

arxiv.org

0

3

14

arXiv math.LO Logic

@mathLOb

10 months

Jeffrey Bergfalk, Chris Lambie-Hanson, Jan Šaroch: Whitehead's problem and condensed mathematics

Whitehead's problem and condensed mathematics

One of the better-known independence results in general mathematics is Shelah's solution to Whitehead's problem of whether $\mathrm{Ext}^1(A,\mathbb{Z})=0$ implies that an abelian group $A$ is...

arxiv.org

0

4

14

arXiv math.LO Logic

@mathLOb

4 years

Gabriel Goldberg: The uniqueness of elementary embeddings

The uniqueness of elementary embeddings

Much of the theory of large cardinals beyond a measurable cardinal concerns the structure of elementary embeddings of the universe of sets into inner models. This paper seeks to answer the...

arxiv.org

1

2

14

arXiv math.LO Logic

@mathLOb

3 years

Sandra Müller: The consistency strength of determinacy when all sets are universally Baire

1

5

14

arXiv math.LO Logic

@mathLOb

1 year

Jorge Antonio Cruz Chapital, Tatsuya Goto, Yusuke Hayashi: Game-theoretic variants of cardinal invariants

Game-theoretic variants of cardinal invariants

We investigate game-theoretic variants of cardinal invariants of the continuum. The invariants we treat are the splitting number $\mathfrak{s}$, the reaping number $\mathfrak{r}$, the bounding...

arxiv.org

0

8

14

arXiv math.LO Logic

@mathLOb

10 months

Haruka Kogure, Taishi Kurahashi: Interpolation properties for the bimodal provability logic $\mathbf{GR}$

Interpolation properties for the bimodal provability logic $\mathbf{GR}$

We study interpolation properties for Shavrukov's bimodal logic $\mathbf{GR}$ of usual and Rosser provability predicates. For this purpose, we introduce a new sublogic $\mathbf{GR}^\circ$ of...

arxiv.org

0

2

12

arXiv math.LO Logic

@mathLOb

1 year

Mark Carney: Computability and Tiling Problems

Computability and Tiling Problems

In this thesis we will present and discuss various results pertaining to tiling problems and mathematical logic, specifically computability theory. We focus on Wang prototiles, as defined in [32]....

arxiv.org

2

5

13

arXiv math.LO Logic

@mathLOb

2 years

Kenta Tsukuura: Prikry-type forcings after collapsing a huge cardinal

Prikry-type forcings after collapsing a huge cardinal

Some models of combinatorial principles have been obtained by collapsing a huge cardinal in the case of the successors of regular cardinals. For example, saturated ideals, Chang's conjecture,...

arxiv.org

1

7

13

arXiv math.LO Logic

@mathLOb

10 months

Juan P. Aguilera, Corey Bacal Switzer: Reflection Properties of Ordinals in Generic Extensions

Reflection Properties of Ordinals in Generic Extensions

We study the question of when a given countable ordinal $α$ is $Σ^1_n$- or $Π^1_n$-reflecting in models which are neither $\mathsf{PD}$ models nor the constructible universe, focusing...

arxiv.org

0

6

13

arXiv math.LO Logic

@mathLOb

6 months

Wesley H. Holliday: Modal logic, fundamentally

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4

13