Restricted polynomial induction versus ordinary induction
Volume 242 / 2018
Fundamenta Mathematicae 242 (2018), 75-92
MSC: Primary 03F30; Secondary 03F40.
DOI: 10.4064/fm323-10-2017
Published online: 26 February 2018
Abstract
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.
