On collection schemes and Gaifman's splitting theorem

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2024-11-10 DOI:10.1002/malq.202400021

Taishi Kurahashi, Yoshiaki Minami

引用次数: 0

Abstract

We study model theoretic characterizations of various collection schemes over ${PA}^{-}$ from the viewpoint of Gaifman's splitting theorem. Among other things, we prove that for any $n \geq 0$ and $M ⊧ {PA}^{-}$ , the following are equivalent:

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关于集合格式和Gaifman的分裂定理

我们从盖夫曼分裂定理的角度研究了 PA - $\mathsf {PA}^-$ 上各种集合方案的模型论特征。其中，我们证明了对于任意 n ≥ 0 $n \ge 0$ 和 M ⊧ PA - $M \models \mathsf {PA}^-$ ，以下内容是等价的：

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.