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December 2010 Infinite substructure lattices of models of Peano Arithmetic
James H. Schmerl
J. Symbolic Logic 75(4): 1366-1382 (December 2010). DOI: 10.2178/jsl/1286198152

Abstract

Bounded lattices (that is lattices that are both lower bounded and upper bounded) form a large class of lattices that include all distributive lattices, many nondistributive finite lattices such as the pentagon lattice N5, and all lattices in any variety generated by a finite bounded lattice. Extending a theorem of Paris for distributive lattices, we prove that if L is an ℵ0-algebraic bounded lattice, then every countable nonstandard model ℳ of Peano Arithmetic has a cofinal elementary extension 𝒩 such that the interstructure lattice Lt(𝒩/ℳ) is isomorphic to L.

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James H. Schmerl. "Infinite substructure lattices of models of Peano Arithmetic." J. Symbolic Logic 75 (4) 1366 - 1382, December 2010. https://doi.org/10.2178/jsl/1286198152

Information

Published: December 2010
First available in Project Euclid: 4 October 2010

zbMATH: 1207.03047
MathSciNet: MR861427
Digital Object Identifier: 10.2178/jsl/1286198152

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 4 • December 2010
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