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On extensions of models of strong fragments of arithmetic


Author: Roman Kossak
Journal: Proc. Amer. Math. Soc. 108 (1990), 223-232
MSC: Primary 03F30; Secondary 03C62, 03H15
MathSciNet review: 984802
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0984802-2
Keywords: fragments of arithmetic, recursive saturation, end extensions, cofinal extensions, automorphisms
Article copyright: © Copyright 1990 American Mathematical Society