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

Mathematical Logic Quarterly 50 (6):533-539 (2004)
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Abstract

This paper concerns intermediate structure lattices Lt, where [MATHEMATICAL SCRIPT CAPITAL 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 for some almost minimal elementary end extension of [MATHEMATICAL SCRIPT CAPITAL N]. If T is a completion of PA and L is a finite lattice, then: If some model of T attains L, then every countable model of T does. If some rather classless, ℵ1-saturated model of T attains L, then every model of T does

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10.1002/malq.200310118

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The Diversity of Minimal Cofinal Extensions.James H. Schmerl - 2022 - Notre Dame Journal of Formal Logic 63 (4):493-514.

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