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

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

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

MathSciNet review:
984802

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Abstract | References | Similar Articles | Additional Information

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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*Models with the*$\omega$

*-property*, to appear in Journal of Symbolic Logic.

*Models of arithmetic*, Ph.D. Thesis, Manchester 1978.

*A note on the end extension problem*, (to appear).

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Keywords:
fragments of arithmetic,
recursive saturation,
end extensions,
cofinal extensions,
automorphisms

Article copyright:
© Copyright 1990
American Mathematical Society