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(2022)
Models of Arithmetic
- Publisher
- Springer Journals
- Copyright
- Copyright © 2014 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-014-0368-9
- Publisher site
- See Article on Publisher Site
Abstract
This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and least number axiom schemes to formulas which are $${\Delta_1}$$ Δ 1 provably in an arithmetic theory T. In particular, we determine the provably total computable functions of this kind of theories. As an application, we obtain a reduction of the problem whether $${I\Delta_0 + \neg \mathit{exp}}$$ I Δ 0 + ¬ exp implies $${B\Sigma_1}$$ B Σ 1 to a purely recursion-theoretic question.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Jan 24, 2014