Abstract
AbstractThis paper concerns intermediate structure lattices Lt(𝒩/ℳ︁), where 𝒩 is an almost minimal elementary end extension of the model ℳ︁ of Peano Arithmetic. For the purposes of this abstract only, let us say that ℳ︁ attains L if L ≅ Lt(𝒩/ℳ︁) 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)
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