On Extensions of Models of Strong Fragments of Arithmetic
Roman Kossak · Proceedings of the American Mathematical Society · 1990
Using a weak notion of recursive saturation (not always semiregularity) we prove that there are no finitely generated countable models of $B\Sigma _n { + eg I{\Sigma _n}( {n > 0} )}$. We consider the problem of not almost semiregularity of models of $I{\Sigma _n} + eg B{\Sigma _{n + 1}}$ . 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.