Models of expansions of N with no end extensions

Saharon Shelah

doi:10.1002/malq.200910129

Models of expansions of N with no end extensions

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of N such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of N such that expanding N by any uncountably many of them suffice. Also we find arithmetically closed A with no ultrafilter on it with suitable definability demand (related to being Ramsey).

Original language	English
Pages (from-to)	341-365
Number of pages	25
Journal	Mathematical Logic Quarterly
Volume	57
Issue number	4
DOIs	https://doi.org/10.1002/malq.200910129
State	Published - Aug 2011

Keywords

End extensions
Forcing with creatures
Models of Peano arithmetic

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10.1002/malq.200910129

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KW - Models of Peano arithmetic

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Models of expansions of N with no end extensions

Abstract

Keywords

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