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Reflection Principles, Generic Large Cardinals, and the Continuum Problem Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Rosser Provability and the Second Incompleteness Theorem

Author : Taishi Kurahashi

Published in: Advances in Mathematical Logic

Publisher: Springer Nature Singapore

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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.

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previous chapter Interpolation Properties for Sacchetti’s Logics
next chapter On Takeuti’s Early View of the Concept of Set
Footnotes
1
Introducing this schematic consistency statement \(\mathsf{Con}_{\mathrm{Pr}_T}^S\) was proposed by the referee.
 
2
This means that \(T \nvdash \mathsf{Con}_{\mathrm{Pr}_T}(\varphi )\) for some formula \(\varphi \).
 
3
This is pointed out by the referee.
 
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Metadata
Title
Rosser Provability and the Second Incompleteness Theorem
Author
Taishi Kurahashi
Copyright Year
2021
Publisher
Springer Nature Singapore
Book
Advances in Mathematical Logic

Print ISBN: 978-981-16-4172-5

Electronic ISBN: 978-981-16-4173-2

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-981-16-4173-2_4

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