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Models of expansions of with no end extensions

✍ Scribed by Saharon Shelah

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 297 KB
Volume: 57
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200910129

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✦ Synopsis

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).

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