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

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 ≅ 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, ℵ₁-saturated model of T attains L, then every model of T does. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]