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1635 found
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  1. Extension, Translation, and the Cantor-Bernstein Property.Thomas William Barrett & Hans Halvorson - manuscript
    The purpose of this paper is to examine in detail a particularly interesting pair of first-order theories. In addition to clarifying the overall geography of notions of equivalence between theories, this simple example yields two surprising conclusions about the relationships that theories might bear to one another. In brief, we see that theories lack both the Cantor-Bernstein and co-Cantor-Bernstein properties.
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  2. What makes a `good' modal theory of sets?Neil Barton - manuscript
    I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...)
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  3. A BIBLIOGRAPHY: JOHN CORCORAN's PUBLICATIONS ON ARISTOTLE 1972–2015.John Corcoran - manuscript
    This presentation includes a complete bibliography of John Corcoran’s publications devoted at least in part to Aristotle’s logic. Sections I–IV list 20 articles, 43 abstracts, 3 books, and 10 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article that antedates Corcoran’s Aristotle’s studies and the Journal of Symbolic Logic article first reporting his original results; it ends with works published in 2015. A few of the items are annotated with endnotes connecting them with (...)
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  4. Zeno Paradox, Unexpected Hanging Paradox (Modeling of Reality & Physical Reality, A Historical-Philosophical view).Farzad Didehvar - manuscript
    . In our research about Fuzzy Time and modeling time, "Unexpected Hanging Paradox" plays a major role. Here, we compare this paradox to the Zeno Paradox and the relations of them with our standard models of continuum and Fuzzy numbers. To do this, we review the project "Fuzzy Time and Possible Impacts of It on Science" and introduce a new way in order to approach the solutions for these paradoxes. Additionally, we have a more general discussion about paradoxes, as Philosophical (...)
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  5. Computational reverse mathematics and foundational analysis.Benedict Eastaugh - manuscript
    Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which explores the limits of different foundations for mathematics in a formally precise manner. This paper gives a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice. It then shows how this account can be fruitfully applied in the (...)
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  6. Partitions and Objective Indefiniteness.David Ellerman - manuscript
    Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...)
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  7. Algunos tópicos de Lógica matemática y los Fundamentos de la matemática.Franklin Galindo - manuscript
    En este trabajo matemático-filosófico se estudian cuatro tópicos de la Lógica matemática: El método de construcción de modelos llamado Ultraproductos, la Propiedad de Interpolación de Craig, las Álgebras booleanas y los Órdenes parciales separativos. El objetivo principal del mismo es analizar la importancia que tienen dichos tópicos para el estudio de los fundamentos de la matemática, desde el punto de vista del platonismo matemático. Para cumplir con tal objetivo se trabajará en el ámbito de la Matemática, de la Metamatemática y (...)
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  8. Soundness does not come for free (if at all).Kaave Lajevardi & Saeed Salehi - manuscript
    We respond to some of the points made by Bennet and Blanck (2022) concerning a previous publication of ours (2021).
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  9. What is Mathematics: Gödel's Theorem and Around (Edition 2015).Karlis Podnieks - manuscript
    Introduction to mathematical logic. Part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.
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  10. Random Formula Generators.Ariel Jonathan Roffé & Joaquín Toranzo Calderón - manuscript
    In this article, we provide three generators of propositional formulae for arbitrary languages, which uniformly sample three different formulae spaces. They take the same three parameters as input, namely, a desired depth, a set of atomics and a set of logical constants (with specified arities). The first generator returns formulae of exactly the given depth, using all or some of the propositional letters. The second does the same but samples up-to the given depth. The third generator outputs formulae with exactly (...)
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  11. Category Theory: A Gentle Introduction.Peter Smith - manuscript
    This Gentle Introduction is very much still work in progress. Roughly aimed at those who want something a bit more discursive, slower-moving, than Awodey's or Leinster's excellent books. -/- The current [Jan 2018] version is 291pp.
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  12. Provably games.J. P. Aguilera & D. W. Blue - forthcoming - Journal of Symbolic Logic:1-22.
    We isolate two abstract determinacy theorems for games of length $\omega_1$ from work of Neeman and use them to conclude, from large-cardinal assumptions and an iterability hypothesis in the region of measurable Woodin cardinals thatif the Continuum Hypothesis holds, then all games of length $\omega_1$ which are provably $\Delta_1$ -definable from a universally Baire parameter are determined;all games of length $\omega_1$ with payoff constructible relative to the play are determined; andif the Continuum Hypothesis holds, then there is a model of (...)
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  13. Strong Compactness, Square, Gch, and Woodin Cardinals.Arthur W. Apter - forthcoming - Journal of Symbolic Logic:1-9.
    We show the consistency, relative to the appropriate supercompactness or strong compactness assumptions, of the existence of a non-supercompact strongly compact cardinal $\kappa _0$ (the least measurable cardinal) exhibiting properties which are impossible when $\kappa _0$ is supercompact. In particular, we construct models in which $\square _{\kappa ^+}$ holds for every inaccessible cardinal $\kappa $ except $\kappa _0$, GCH fails at every inaccessible cardinal except $\kappa _0$, and $\kappa _0$ is less than the least Woodin cardinal.
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  14. Dependent choice, properness, and generic absoluteness.David Asperó & Asaf Karagila - forthcoming - Review of Symbolic Logic:1-25.
    We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals, even with respect to $\mathsf {DC}$ -preserving symmetric submodels of forcing extensions. Hence, $\mathsf {ZF}+\mathsf {DC}$ not only provides the right framework for developing classical analysis, but is also the right base theory over which to safeguard truth in analysis from the independence phenomenon in the presence of (...)
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  15. How Much Propositional Logic Suffices for Rosser’s Essential Undecidability Theorem?Guillermo Badia, Petr Cintula, Petr Hajek & Andrew Tedder - forthcoming - Review of Symbolic Logic:1-18.
    In this paper we explore the following question: how weak can a logic be for Rosser's essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson's Q is essentially undecidable in intuitionistic logic, and P. Hajek proved it in the fuzzy logic BL for Grzegorczyk's variant of Q which interprets the arithmetic operations as non-total non-functional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...)
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  16. How Much Propositional Logic Suffices for Rosser's Essential Undecidability Theorem?Guillermo Badia, Petr Cintula, Petr Hajek & Andrew Tedder - forthcoming - Review of Symbolic Logic.
    In this paper we explore the following question: how weak can a logic be for Rosser’s essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson’s Q is essentially undecidable in intuitionistic logic, and P. Hájek proved it in the fuzzy logic BL for Grzegorczyk’s variant of Q which interprets the arithmetic operations as nontotal nonfunctional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...)
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  17. Defining Measures in a Mereological Space.Giuseppina Barbieri & Giangiacomo Gerla - forthcoming - Logic and Logical Philosophy:1.
    We explore the notion of a measure in a mereological structure and we deal with the difficulties arising. We show that measure theory on connection spaces is closely related to measure theory on the class of ortholattices and we present an approach akin to Dempster’s and Shafer’s. Finally, the paper contains some suggestions for further research.
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  18. Characterizing existence of a measurable cardinal via modal logic.G. Bezhanishvili, N. Bezhanishvili, J. Lucero-Bryan & J. van Mill - forthcoming - Journal of Symbolic Logic:1-15.
    We prove that the existence of a measurable cardinal is equivalent to the existence of a normal space whose modal logic coincides with the modal logic of the Kripke frame isomorphic to the powerset of a two element set.
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  19. The additive groups of ℤ and ℚ with predicates for being square‐free.Neer Bhardwaj & Minh Chieu Tran - forthcoming - Journal of Symbolic Logic:1-26.
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  20. Frege’s Theory of Real Numbers: A Consistent Rendering.Francesca Boccuni & Marco Panza - forthcoming - Review of Symbolic Logic:1-44.
    Frege's definition of the real numbers, as envisaged in the second volume of Grundgesetze der Arithmetik, is fatally flawed by the inconsistency of Frege's ill-fated Basic Law V. We restate Frege's definition in a consistent logical framework and investigate whether it can provide a logical foundation of real analysis. Our conclusion will deem it doubtful that such a foundation along the lines of Frege's own indications is possible at all.
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  21. Inferential Quantification and the ω-rule.Constantin C. Brîncuș - forthcoming - In Antonio D’Aragona (ed.), Perspectives on Deduction.
    Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...)
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  22. The Well-Ordered Society under Crisis: A Formal Analysis of Public Reason vs. Convergence Discourse.Hun Chung - forthcoming - American Journal of Political Science:1-20.
    A well-ordered society faces a crisis whenever a sufficient number of noncompliers enter into the political system. This has the potential to destabilize liberal democratic political order. This article provides a formal analysis of two competing solutions to the problem of political stability offered in the public reason liberalism literature—namely, using public reason or using convergence discourse to restore liberal democratic political order in the well-ordered society. The formal analyses offered in this article show that using public reason fails completely, (...)
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  23. On a Problem of Friedman and its Solution by Rybakov.Jeroen P. Goudsmit - forthcoming - Bulletin of Symbolic Logic:1-48.
    Rybakov (1984a) proved that the admissible rules of IPC are decidable. We give a proof of the same theorem, using the same core idea, but couched in the many notions that have been developed in the mean time. In particular, we illustrate how the argument can be interpreted as using refinements of the notions of exactness and extendibility.
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  24. Free Definite Description Theory – Sequent Calculi and Cut Elimination.Andrzej Indrzejczak - forthcoming - Logic and Logical Philosophy:1.
    We provide an application of a sequent calculus framework to the formalization of definite descriptions. It is a continuation of research undertaken in [20, 22]. In the present paper a so-called free description theory is examined in the context of different kinds of free logic, including systems applied in computer science and constructive mathematics for dealing with partial functions. It is shown that the same theory in different logics may be formalised by means of different rules and gives results of (...)
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  25. On Shavrukov’s Non-Isomorphism Theorem for Diagonalizable Algebras.Evgeny A. Kolmakov - forthcoming - Review of Symbolic Logic:1-38.
    We prove a strengthened version of Shavrukov’s result on the non-isomorphism of diagonalizable algebras of two $\Sigma _1$ -sound theories, based on the improvements previously found by Adamsson. We then obtain several corollaries to the strengthened result by applying it to various pairs of theories and obtain new non-isomorphism examples. In particular, we show that there are no surjective homomorphisms from the algebra $(\mathfrak {L}_T, \Box _T\Box _T)$ onto the algebra $(\mathfrak {L}_T, \Box _T)$. The case of bimodal diagonalizable algebras (...)
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  26. Groups of Worldview Transformations Implied by Einstein’s Special Principle of Relativity over Arbitrary Ordered Fields.Judit X. Madarász, Mike Stannett & Gergely Székely - forthcoming - Review of Symbolic Logic:1-28.
    In 1978, Yu. F. Borisov presented an axiom system using a few basic assumptions and four explicit axioms, the fourth being a formulation of the relativity principle; and he demonstrated that this axiom system had (up to choice of units) only two models: a relativistic one in which worldview transformations are Poincaré transformations and a classical one in which they are Galilean. In this paper, we reformulate Borisov’s original four axioms within an intuitively simple, but strictly formal, first-order logic framework, (...)
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  27. The permutations with N_ non-fixed points and the sequences with length _N of a set.Jukkrid Nuntasri & Pimpen Vejjajiva - forthcoming - Journal of Symbolic Logic:1-10.
    We write$\mathcal {S}_n(A)$for the set of permutations of a setAwithnnon-fixed points and$\mathrm {{seq}}^{1-1}_n(A)$for the set of one-to-one sequences of elements ofAwith lengthnwherenis a natural number greater than$1$. With the Axiom of Choice,$|\mathcal {S}_n(A)|$and$|\mathrm {{seq}}^{1-1}_n(A)|$are equal for all infinite setsA. Among our results, we show, in ZF, that$|\mathcal {S}_n(A)|\leq |\mathrm {{seq}}^{1-1}_n(A)|$for any infinite setAif${\mathrm {AC}}_{\leq n}$is assumed and this assumption cannot be removed. In the other direction, we show that$|\mathrm {{seq}}^{1-1}_n(A)|\leq |\mathcal {S}_{n+1}(A)|$for any infinite setAand the subscript$n+1$cannot be reduced ton. Moreover, (...)
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  28. The first-order logic of CZF is intuitionistic first-order logic.Robert Passmann - forthcoming - Journal of Symbolic Logic:1-23.
    We prove that the first-order logic of CZF is intuitionistic first-order logic. To do so, we introduce a new model of transfinite computation (Set Register Machines) and combine the resulting notion of realisability with Beth semantics. On the way, we also show that the propositional admissible rules of CZF are exactly those of intuitionistic propositional logic.
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  29. Automated Proof-searching for Strong Kleene Logic and its Binary Extensions via Correspondence Analysis.Yaroslav Petrukhin & Vasilyi Shangin - forthcoming - Logic and Logical Philosophy:1.
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  30. Variations on determinacy and.Ramez L. Sami - forthcoming - Journal of Symbolic Logic:1-10.
  31. Primitive recursive equivalence relations and their primitive recursive complexity.Luca San Mauro, Nikolay Bazhenov, Keng Meng Ng & Andrea Sorbi - forthcoming - Computability.
    The complexity of equivalence relations has received much attention in the recent literature. The main tool for such endeavour is the following reducibility: given equivalence relations R and S on natural numbers, R is computably reducible to S if there is a computable function f:ω→ω that induces an injective map from R-equivalence classes to S-equivalence classes. In order to compare the complexity of equivalence relations which are computable, researchers considered also feasible variants of computable reducibility, such as the polynomial-time reducibility. (...)
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  32. Definability Aspects of the Denjoy Integral.Walsh Sean - forthcoming - Fundamenta Mathematicae.
    The Denjoy integral is an integral that extends the Lebesgue integral and can integrate any derivative. In this paper, it is shown that the graph of the indefinite Denjoy integral f↦∫xaf is a coanalytic non-Borel relation on the product space M[a,b]×C[a,b], where M[a,b] is the Polish space of real-valued measurable functions on [a,b] and where C[a,b] is the Polish space of real-valued continuous functions on [a,b]. Using the same methods, it is also shown that the class of indefinite Denjoy integrals, (...)
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  33. Almost Theorems of Hyperarithmetic Analysis.Richard A. Shore - forthcoming - Journal of Symbolic Logic:1-33.
    Theorems of hyperarithmetic analysis (THAs) occupy an unusual neighborhood in the realms of reverse mathematics and recursion theoretic complexity. They lie above all the fixed (recursive) iterations of the Turing Jump but below ATR $_{0}$ (and so $\Pi _{1}^{1}$ -CA $_{0}$ or the hyperjump). There is a long history of proof theoretic principles which are THAs. Until Barnes, Goh, and Shore [ta] revealed an array of theorems in graph theory living in this neighborhood, there was only one mathematical denizen. In (...)
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  34. Natural formalization: Deriving the Cantor-Bernstein theorem in zf.Wilfried Sieg & Patrick Walsh - forthcoming - Review of Symbolic Logic:1-44.
    Natural Formalization proposes a concrete way of expanding proof theory from the meta-mathematical investigation of formal theories to an examination of “the concept of the specifically mathematical proof.” Formal proofs play a role for this examination in as much as they reflect the essential structure and systematic construction of mathematical proofs. We emphasize three crucial features of our formal inference mechanism: (1) the underlying logical calculus is built for reasoning with gaps and for providing strategic directions, (2) the mathematical frame (...)
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  35. The characterization of Weihrauch reducibility in systems containing e-pa ω + qf-ac0;0.Patrick Uftring - forthcoming - Journal of Symbolic Logic:1-35.
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  36. An incompleteness theorem via ordinal analysis.James Walsh - forthcoming - Journal of Symbolic Logic:1-17.
    We present an analogue of Gödel's second incompleteness theorem for systems of second-order arithmetic. Whereas Gödel showed that sufficiently strong theories that are $\Pi^0_1$-sound and $\Sigma^0_1$-definable do not prove their own $\Pi^0_1$-soundness, we prove that sufficiently strong theories that are $\Pi^1_1$-sound and $\Sigma^1_1$-definable do not prove their own $\Pi^1_1$-soundness. Our proof does not involve the construction of a self-referential sentence but rather relies on ordinal analysis.
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  37. Bayesian merging of opinions and algorithmic randomness.Francesca Zaffora Blando - forthcoming - British Journal for the Philosophy of Science.
    We study the phenomenon of merging of opinions for computationally limited Bayesian agents from the perspective of algorithmic randomness. When they agree on which data streams are algorithmically random, two Bayesian agents beginning the learning process with different priors may be seen as having compatible beliefs about the global uniformity of nature. This is because the algorithmically random data streams are of necessity globally regular: they are precisely the sequences that satisfy certain important statistical laws. By virtue of agreeing on (...)
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  38. Notice of Retraction: Pseudofinite difference field.Tingxiang Zou - forthcoming - Journal of Mathematical Logic:1993001.
    Journal of Mathematical Logic, Ahead of Print.
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  39. Reverse Mathematics.Benedict Eastaugh - 2024 - The Stanford Encyclopedia of Philosophy.
    Reverse mathematics is a program in mathematical logic that seeks to give precise answers to the question of which axioms are necessary in order to prove theorems of "ordinary mathematics": roughly speaking, those concerning structures that are either themselves countable, or which can be represented by countable "codes". This includes many fundamental theorems of real, complex, and functional analysis, countable algebra, countable infinitary combinatorics, descriptive set theory, and mathematical logic. This entry aims to give the reader a broad introduction to (...)
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  40. Formal differential variables and an abstract chain rule.Samuel Alexander - 2023 - Proceedings of the ACMS 23.
    One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated differentials and a version of the multivariable chain rule which iterates to any desired level of derivative. We first present this material informally, and later discuss how to make it rigorous (a discussion which touches on formal foundations of calculus). We also suggest a finite calculus chain rule (contrary to Graham, Knuth (...)
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  41. Expanding the Reals by Continuous Functions Adds No Computational Power.Uri Andrews, Julia F. Knight, Rutger Kuyper, Joseph S. Miller & Mariya I. Soskova - 2023 - Journal of Symbolic Logic 88 (3):1083-1102.
    We study the relative computational power of structures related to the ordered field of reals, specifically using the notion of generic Muchnik reducibility. We show that any expansion of the reals by a continuous function has no more computing power than the reals, answering a question of Igusa, Knight, and Schweber [7]. On the other hand, we show that there is a certain Borel expansion of the reals that is strictly more powerful than the reals and such that any Borel (...)
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  42. More on the Preservation of Large Cardinals Under Class Forcing.Joan Bagaria & Alejandro Poveda - 2023 - Journal of Symbolic Logic 88 (1):290-323.
    We prove two general results about the preservation of extendible and $C^{(n)}$ -extendible cardinals under a wide class of forcing iterations (Theorems 5.4 and 7.5). As applications we give new proofs of the preservation of Vopěnka’s Principle and $C^{(n)}$ -extendible cardinals under Jensen’s iteration for forcing the GCH [17], previously obtained in [8, 27], respectively. We prove that $C^{(n)}$ -extendible cardinals are preserved by forcing with standard Easton-support iterations for any possible $\Delta _2$ -definable behaviour of the power-set function on (...)
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  43. Admissibility of Π2-Inference Rules: interpolation, model completion, and contact algebras.Nick Bezhanishvili, Luca Carai, Silvio Ghilardi & Lucia Landi - 2023 - Annals of Pure and Applied Logic 174 (1):103169.
  44. On Sequences of Homomorphisms Into Measure Algebras and the Efimov Problem.Piotr Borodulin–Nadzieja & Damian Sobota - 2023 - Journal of Symbolic Logic 88 (1):191-218.
    For given Boolean algebras$\mathbb {A}$and$\mathbb {B}$we endow the space$\mathcal {H}(\mathbb {A},\mathbb {B})$of all Boolean homomorphisms from$\mathbb {A}$to$\mathbb {B}$with various topologies and study convergence properties of sequences in$\mathcal {H}(\mathbb {A},\mathbb {B})$. We are in particular interested in the situation when$\mathbb {B}$is a measure algebra as in this case we obtain a natural tool for studying topological convergence properties of sequences of ultrafilters on$\mathbb {A}$in random extensions of the set-theoretical universe. This appears to have strong connections with Dow and Fremlin’s result stating (...)
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  45. Strength in coalitions: Community detection through argument similarity.Paola Daniela Budán, Melisa Gisselle Escañuela Gonzalez, Maximiliano Celmo David Budán, Maria Vanina Martinez & Guillermo Ricardo Simari - 2023 - Argument and Computation 14 (3):275-325.
    We present a novel argumentation-based method for finding and analyzing communities in social media on the Web, where a community is regarded as a set of supported opinions that might be in conflict. Based on their stance, we identify argumentative coalitions to define them; then, we apply a similarity-based evaluation method over the set of arguments in the coalition to determine the level of cohesion inherent to each community, classifying them appropriately. Introducing conflict points and attacks between coalitions based on (...)
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  46. Inconcistency of ℕ from a not-finitist point of view.Enrico Pier Giorgio Cadeddu - 2023 - International Journal of Modern Research in Engineering and Technology 8 (10):2.
    Considering the set of natural numbers ℕ, then in the context of Peano axioms, starting from inequalities between finite sets, we find a fundamental contradiction, about the existence of ℕ, from a not-finitist point of view.
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  47. Hilbert Algebras with Hilbert–Galois Connections.Sergio A. Celani & Daniela Montangie - 2023 - Studia Logica 111 (1):113-138.
    In this paper we introduce Hilbert algebras with Hilbert–Galois connections (HilGC-algebras) and we study the Hilbert–Galois connections defined in Heyting algebras, called HGC-algebras. We assign a categorical duality between the category HilGC-algebras with Hilbert homomorphisms that commutes with Hilbert–Galois connections and Hilbert spaces with certain binary relations and whose morphisms are special functional relations. We also prove a categorical duality between the category of Heyting Galois algebras with Heyting homomorphisms that commutes with Hilbert–Galois connections and the category of spectral Heyting (...)
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  48. Invariant measures in simple and in small theories.Artem Chernikov, Ehud Hrushovski, Alex Kruckman, Krzysztof Krupiński, Slavko Moconja, Anand Pillay & Nicholas Ramsey - 2023 - Journal of Mathematical Logic 23 (2).
    We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting of discrete groups (...)
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  49. Constructive strong regularity and the extension property of a compactification.Giovanni Curi - 2023 - Annals of Pure and Applied Logic 174 (1):103154.
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  50. RETRACTED ARTICLE: There are Infinitely Many Mersenne Prime Numbers. Applications of Rasiowa–Sikorski Lemma in Arithmetic (II).Janusz Czelakowski - 2023 - Studia Logica 111 (2):359-359.
    The paper is concerned with the old conjecture that there are infinitely many Mersenne primes. It is shown in the work that this conjecture is true in the standard model of arithmetic. The proof refers to the general approach to first–order logic based on Rasiowa-Sikorski Lemma and the derived notion of a Rasiowa–Sikorski set. This approach was developed in the papers [ 2 – 4 ]. This work is a companion piece to [ 4 ].
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