Zobrazeno 1 - 10
of 63
pro vyhledávání: '"Łełyk, Mateusz"'
Autor:
Gruza, Piotr, Łełyk, Mateusz
We study the structure of the partial order induced by the definability relation on definitions of truth for the language of arithmetic. Formally, a definition of truth is any sentence $\alpha$ which extends a weak arithmetical theory (which we take
Externí odkaz:
http://arxiv.org/abs/2311.13519
Autor:
Łełyk, Mateusz, Wcisło, Bartosz
We investigate abstract model theoretic properties which holds for models in which a truth or satisfaction predicate for a sublanguage of the signature is definable. We analyse in which cases those properties in fact ensure the definability of the re
Externí odkaz:
http://arxiv.org/abs/2304.00370
Autor:
Abdul-Quader, Athar, Łełyk, Mateusz
We study subsets of countable recursively saturated models of $\mathsf{PA}$ which can be defined using pathologies in satisfaction classes. More precisely, we characterize those subsets $X$ such that there is a satisfaction class $S$ where $S$ behave
Externí odkaz:
http://arxiv.org/abs/2303.18069
Autor:
Łelyk, Mateusz, Nicolai, Carlo
G\"odel's Incompleteness Theorems suggest that no single formal system can capture the entirety of one's mathematical beliefs, while pointing at a hierarchy of systems of increasing logical strength that make progressively more explicit those \emph{i
Externí odkaz:
http://arxiv.org/abs/2302.02783
Ali Enayat had asked whether two halves of Disjunctive Correctness (DC) for the compositional truth predicate are conservative over Peano Arithmetic. In this article, we show that the principle "every true disjunction has a true disjunct" is equivale
Externí odkaz:
http://arxiv.org/abs/2108.13718
Autor:
Abdul-Quader, Athar, Łełyk, Mateusz
Publikováno v:
In Annals of Pure and Applied Logic February 2024 175(2)
Autor:
Łełyk, Mateusz, Wcisło, Bartosz
We introduce a principle of local collection for compositional truth predicates and show that it is conservative over the classically compositional theory of truth in the arithmetical setting. This axiom states that upon restriction to formulae of an
Externí odkaz:
http://arxiv.org/abs/2006.11124
Publikováno v:
J. symb. log. 85 (2020) 367-421
Let $\mathcal{T}$ be any of the three canonical truth theories $\textsf{CT}^-$ (Compositional truth without extra induction), $\textsf{FS}^-$ (Friedman--Sheard truth without extra induction), and $\textsf{KF}^-$ (Kripke--Feferman truth without extra
Externí odkaz:
http://arxiv.org/abs/1902.00392
Autor:
Klin, Bartek, Łełyk, Mateusz
Publikováno v:
Logical Methods in Computer Science, Volume 15, Issue 4 (October 29, 2019) lmcs:4389
We study an extension of modal $\mu$-calculus to sets with atoms and we study its basic properties. Model checking is decidable on orbit-finite structures, and a correspondence to parity games holds. On the other hand, satisfiability becomes undecida
Externí odkaz:
http://arxiv.org/abs/1803.06752
Autor:
Łełyk, Mateusz, Wcisło, Bartosz
Publikováno v:
Arch. Math. Logic (2017) 56: 453
In the following paper we propose a model-theoretical way of comparing the "strength" of various truth theories which are conservative over PA. Let $\mathfrak{Th}$ denote the class of models of PA which admit an expansion to a model of theory Th. We
Externí odkaz:
http://arxiv.org/abs/1712.00471