James H. Schmerl

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A hnite. indecomposabic partially ordered set is said to be critically indecomposahlc if. whenever an clement is removed. the resulting induced partially ordered set is not indccomposabic. The same terminology can be applied to graphs. tournaments, or any other relational structure whose relations are binary and irrcflexive. It will be shown in this paper(More)
Recursive saturation has come to play an important part in the model theory of Peano Arithmetic (PA). One of the neater results is the theorem of Smoryfiski and Stavi [16] that recursive saturation is preserved by cofinal extensions. (We give a quite simple proof of this in Corollary 1.3(i).) It is natural to inquire about a converse to this theorem, but(More)
A basic result in the model theory of Peano Arithmetic (PA) is the theorem of MacDowell and Specker [11], which asserts that every model M of PA has an elementary end extension N end M. Phillips [12] observed that the proof of the MacDowell–Specker Theorem yields even more: every modelM of PA has a conservative elementary extensionN M. We let Def(M) be the(More)