Rosser provability and the second incompleteness theorem

TL;DR

This paper explores the limitations of the second incompleteness theorem by constructing specific Rosser provability predicates that meet certain derivability conditions, extending previous work on derivability conditions.

Contribution

It introduces three new Rosser provability predicates satisfying various derivability conditions, advancing understanding of the second incompleteness theorem's boundaries.

Findings

Constructed three Rosser provability predicates meeting derivability conditions

Demonstrated limitations of the second incompleteness theorem with these predicates

Extended previous derivability condition frameworks

Abstract

This paper is a continuation of Arai's paper on derivability conditions for Rosser provability predicates. We investigate the limitations of the second incompleteness theorem by constructing three different Rosser provability predicates satisfying several derivability conditions.