0100489414

open access

Accepted Manuscript

The persistence principle over weak interpretability logic

English (英語)

Mathematical Logic Quarterly

70(1)

37-63

John Wiley & Sons

2024-02

2024-10-27

Published Online: 2023-10-27

We focus on the persistence principle over weak interpretability logic. Our object of study is the logic obtained by adding the persistence principle to weak interpretability logic from several perspectives. Firstly, we prove that this logic enjoys a weak version of the fixed point property. Secondly, we introduce a system of sequent calculus and prove the cut-elimination theorem for it. As a consequence, we prove that the logic enjoys the Craig interpolation property. Thirdly, we show that the logic is the natural basis of a generalization of simplified Veltman semantics, and prove that it has the finite frame property with respect to that semantics. Finally, we prove that it is sound and complete with respect to some appropriate arithmetical semantics.

学術雑誌論文

This is the peer reviewed version of the following article: [Iwata, S., Kurahashi, T. and Okawa, Y. (2024), The persistence principle over weak interpretability logic. Math. Log. Quart., 70: 37-63.], which has been published in final form at [https://doi.org/10.1002/malq.202200020]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.