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March 2008 Nondiversity in substructures
James H. Schmerl
J. Symbolic Logic 73(1): 193-211 (March 2008). DOI: 10.2178/jsl/1208358749

Abstract

For a model ℳ of Peano Arithmetic, let Lt(ℳ) be the lattice of its elementary substructures, and let Lt+(ℳ) be the equivalenced lattice (Lt(ℳ), ≅), where ≅ is the equivalence relation of isomorphism on Lt(ℳ). It is known that Lt+(ℳ) is always a reasonable equivalenced lattice.

Theorem Let L be a finite distributive lattice and let (L,E) be reasonable. If ℳ0 is a nonstandard prime model of PA, then ℳ0 has a cofinal extension ℳ such that Lt+(ℳ) ≅ (L,E).

A general method for proving such theorems is developed which, hopefully, will be able to be applied to some nondistributive lattices.

Citation

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James H. Schmerl. "Nondiversity in substructures." J. Symbolic Logic 73 (1) 193 - 211, March 2008. https://doi.org/10.2178/jsl/1208358749

Information

Published: March 2008
First available in Project Euclid: 16 April 2008

zbMATH: 1141.03014
MathSciNet: MR2387939
Digital Object Identifier: 10.2178/jsl/1208358749

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 1 • March 2008
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