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Restricted polynomial induction versus parameter free ordinary induction

Volume 257 / 2022

Zofia Adamowicz 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.

Authors

  • Zofia AdamowiczMathematical Institute
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail

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