Journal of Symbolic Logic

Infinite substructure lattices of models of Peano Arithmetic

James H. Schmerl

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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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J. Symbolic Logic, Volume 75, Issue 4 (2010), 1366-1382.

First available in Project Euclid: 4 October 2010

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Schmerl, James H. Infinite substructure lattices of models of Peano Arithmetic. J. Symbolic Logic 75 (2010), no. 4, 1366--1382. doi:10.2178/jsl/1286198152.

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