Models of expansions of equation image with no end extensions

Mathematical Logic Quarterly 57 (4):341-365 (2011)
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Abstract

We deal with models of Peano arithmetic. The methods are from creature forcing. We find an expansion of equation image such that its theory has models with no end extensions. In fact there is a Borel uncountable set of subsets of equation image such that expanding equation image by any uncountably many of them suffice. Also we find arithmetically closed equation image with no ultrafilter on it with suitable definability demand. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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10.1002/malq.200910129

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End extensions and numbers of countable models.Saharon Shelah - 1978 - Journal of Symbolic Logic 43 (3):550-562.
A model of peano arithmetic with no elementary end extension.George Mills - 1978 - Journal of Symbolic Logic 43 (3):563-567.

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