End Extensions of Models of Weak Arithmetic Theories

Costas Dimitracopoulos; Vasileios S. Paschalis

doi:10.1215/00294527-3452693

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Home > Journals > Notre Dame J. Formal Logic > Volume 57 > Issue 2 > Article

2016 End Extensions of Models of Weak Arithmetic Theories

Costas Dimitracopoulos, Vasileios S. Paschalis

Notre Dame J. Formal Logic 57(2): 181-193 (2016). DOI: 10.1215/00294527-3452693

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Abstract

We give alternative proofs of results due to Paris and Wilkie concerning the existence of end extensions of countable models of $B\Sigma_{1}$ , that is, the theory of $\Sigma_{1}$ collection.

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Costas Dimitracopoulos. Vasileios S. Paschalis. "End Extensions of Models of Weak Arithmetic Theories." Notre Dame J. Formal Logic 57 (2) 181 - 193, 2016. https://doi.org/10.1215/00294527-3452693

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Received: 18 September 2013; Accepted: 6 January 2014; Published: 2016

First available in Project Euclid: 7 January 2016

zbMATH: 06585182

MathSciNet: MR3482741

Digital Object Identifier: 10.1215/00294527-3452693

Subjects:

Primary: 03C62

Secondary: 03F30 , 03H15

Keywords: arithmetized completeness theorem , end extensions , fragments of Peano arithmetic

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Vol.57 • No. 2 • 2016

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Costas Dimitracopoulos, Vasileios S. Paschalis "End Extensions of Models of Weak Arithmetic Theories," Notre Dame Journal of Formal Logic, Notre Dame J. Formal Logic 57(2), 181-193, (2016)

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