PP-2016-31: A Solovay function for the least 1-inconsistent subtheory of PA

PP-2016-31: Henk, Paula and Shavrukov, V. Yu. (2016) A Solovay function for the least 1-inconsistent subtheory of PA. [Report]

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Abstract

We consider the theory IΣμ, where μ is the least x such that IΣx together with all true Π1-sentences is inconsistent. We show that the provability logic of IΣμ coincides with that of PA, i.e. the Gödel–Löb provability logic GL. While arithmetical completeness of GL with respect to PA is established by using a single Solovay function, our proof for IΣμ relies on a uniformly defined infinite sequence of such functions.

Item Type: Report
Report Nr: PP-2016-31
Series Name: Prepublication (PP) Series
Year: 2016
Uncontrolled Keywords: Provability logic, Peano Arithmetic
Subjects: Logic
Depositing User: Paula Henk
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/567

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