论文信息 - Infinite substructure lattices of models of Peano Arithmetic

Infinite substructure lattices of models of Peano Arithmetic

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 N 5 . 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 ℵ 0 -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 .

James H. Schmerl | J. Schmerl

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