限制多项式归纳法与无参数普通归纳法

IF 0.5 3区数学 Q3 MATHEMATICS

Fundamenta Mathematicae Pub Date : 2022-01-01 DOI:10.4064/fm887-10-2021

Z. Adamowicz

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引用次数: 0

摘要

。这篇论文是[Z]的延续。Adamowicz,基金。数学学报，242(2018)。我们一方面考虑后继运算、加法运算和乘法运算不能证明为全的算术理论和有界算术理论I∆0的片段之间的保守性问题，另一方面考虑这些理论对Buss有界算术s2的子理论的推广。这些问题与I∆0的有限公理化性问题有关，其中不假设所有的运算。

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Restricted polynomial induction versus parameter free ordinary induction

. The paper is a continuation of [Z. Adamowicz, Fund. Math. 242 (2018)]. We consider conservativity questions between, on the one hand, arithmetical theories in which the operations of successor, addition and multiplication are not provably total and which are fragments of the bounded arithmetic theory I ∆ 0 and, on the other hand, exten-sions of those theories to subtheories of Buss’s bounded arithmetic S 2 . These questions are related to the problem of ﬁnite axiomatizability of a version of I ∆ 0 in which the totality of the operations is not assumed.

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来源期刊

Fundamenta Mathematicae 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： FUNDAMENTA MATHEMATICAE concentrates on papers devoted to Set Theory, Mathematical Logic and Foundations of Mathematics, Topology and its Interactions with Algebra, Dynamical Systems.