Substructure lattices and almost minimal end extensions of models of Peano arithmetic

摘要

This paper concerns intermediate structure lattices Lt(N/M), where N is an almost minimal elementary end extension of the model M of Peano Arithmetic. For the purposes of this abstract only, let us say that M attains L if L approx= Lt(N/M) for some almost minimal elementary end extension of N. If T is a completion of PA and L is a finite lattice, then: (A) If some model of T attains L, then every countable model of T does.(B) If some rather classless, N_1-saturated model of T attains L, then every model of T does.