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Infinite substructure lattices of models of Peano Arithmetic

Published online by Cambridge University Press:  12 March 2014

James H. Schmerl
James H. Schmerl*
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, USA. E-mail: schmerl@math.uconn.edu
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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 of Peano Arithmetic has a cofinal elementary extension such that the interstructure lattice Lt(/) is isomorphic to L.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 4 , December 2010 , pp. 1366 - 1382
Copyright
Copyright © Association for Symbolic Logic 2010

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