PP201631: Henk, Paula and Shavrukov, V. Yu. (2016) A Solovay function for the least 1inconsistent 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 Π1sentences 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:  PP201631 
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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