On extensions of models of strong fragments of arithmetic

Kossak, Roman

doi:10.1090/S0002-9939-1990-0984802-2

On extensions of models of strong fragments of arithmetic
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by Roman Kossak

Proc. Amer. Math. Soc. 108 (1990), 223-232

DOI: https://doi.org/10.1090/S0002-9939-1990-0984802-2

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Correction: Proc. Amer. Math. Soc. 112 (1991), 913-914.

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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A note on the end extension problem