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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On extensions of models of strong fragments of arithmetic
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by Roman Kossak PDF
Proc. Amer. Math. Soc. 108 (1990), 223-232 Request permission

Abstract:

Using a weak notion of recursive saturation (not always semiregularity) we prove that there are no finitely generated countable models of $B\Sigma _n { + \neg I{\Sigma _n}( {n > 0} )}$. We consider the problem of not almost semiregularity of models of $I{\Sigma _n} + \neg B{\Sigma _{n + 1}}$ . From a partial solution to this problem we deduce a generalization of the theorem of Smorynski and Stavi on cofinal extensions of recursively saturated models of arithmetic.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 223-232
  • MSC: Primary 03F30; Secondary 03C62, 03H15
  • DOI: https://doi.org/10.1090/S0002-9939-1990-0984802-2
  • MathSciNet review: 984802