Restricted polynomial induction versus parameter free ordinary induction
Volume 257 / 2022
Fundamenta Mathematicae 257 (2022), 167-187
MSC: Primary 03F30; Secondary 03F40.
DOI: 10.4064/fm887-10-2021
Published online: 13 January 2022
Abstract
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 $I\Delta _0$ and, on the other hand, extensions 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 $I\Delta _0$ in which the totality of the operations is not assumed.
