Zobrazeno 1 - 10
of 195
pro vyhledávání: '"03H15"'
Autor:
Sun, Mengzhou
We investigate the end extendibility of models of arithmetic with restricted elementarity. By utilizing the restricted ultrapower construction in the second-order context, for each $n\in\mathbb{N}$ and any countable model of $\mathrm{B}\Sigma_{n+2}$,
Externí odkaz:
http://arxiv.org/abs/2409.03527
Autor:
Wcisło, Bartosz
Fujimoto and Halbach had introduced a novel theory of type-free truth CD which satisfies full classical compositional clauses for connectives and quantifiers. Answering their question, we show that the induction-free variant of that theory is conserv
Externí odkaz:
http://arxiv.org/abs/2408.01198
Autor:
Abdul-Quader, Athar, Kossak, Roman
The lattice problem for models of Peano Arithmetic ($\mathsf{PA}$) is to determine which lattices can be represented as lattices of elementary submodels of a model of $\mathsf{PA}$, or, in greater generality, for a given model $\mathcal{M}$, which la
Externí odkaz:
http://arxiv.org/abs/2406.06338
Autor:
Wcisło, Bartosz
It is an open question whether compositional truth with the principle of propositional soundness ,,all arithmetical sentences which are propositional tautologies are true'' is conservative over its arithmetical base theory. In this article, we show t
Externí odkaz:
http://arxiv.org/abs/2405.13942
Autor:
Wcisło, Bartosz
Answering a question of Kaye, we show that the compositional truth theory with a full collection scheme is conservative over Peano Arithmetic. We demonstrate it by showing that countable models of compositional truth which satisfy the internal induct
Externí odkaz:
http://arxiv.org/abs/2403.19367
Autor:
Šobot, Boris
An extension of the divisibility relation on $\mathbb{N}$ to the set $\beta\mathbb{N}$ of ultrafilters on $\mathbb{N}$ was defined and investigated in several papers during the last ten years. Here we make a survey of results obtained so far, adding
Externí odkaz:
http://arxiv.org/abs/2401.02302
Autor:
Zapryagaev, Alexander
B\"uchi arithmetics $\mathop{\mathbf{BA}}\nolimits_n$, $n\ge 2$, are extensions of Presburger arithmetic with an unary functional symbol $V_n(x)$ denoting the largest power of $n$ that divides $x$. We explore the structure of non-standard models of B
Externí odkaz:
http://arxiv.org/abs/2312.13757
Autor:
Šobot, Boris
A divisibility relation on ultrafilters is defined as follows: ${\cal F}\hspace{1mm}\widetilde{\mid}\hspace{1mm}{\cal G}$ if and only if every set in $\cal F$ upward closed for divisibility also belongs to $\cal G$. After describing the first $\omega
Externí odkaz:
http://arxiv.org/abs/2306.00101
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:
Kovalyov, Konstantin
In this paper we consider some fragments of $\mathsf{IOpen}$ (Robinson arithmetic $\mathsf Q$ with induction for quantifier-free formulas) proposed by Harvey Friedman and answer some questions he asked about these theories. We prove that $\mathsf{I(l
Externí odkaz:
http://arxiv.org/abs/2304.00282