Infinite substructure lattices of models of Peano Arithmetic

Journal of Symbolic Logic 75 (4):1366-1382 (2010)
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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 of Peano Arithmetic has a cofinal elementary extension such that the interstructure lattice Lt( / ) is isomorphic to L



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Arithmetically Saturated Models of Arithmetic.Roman Kossak & James H. Schmerl - 1995 - Notre Dame Journal of Formal Logic 36 (4):531-546.

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Substructure lattices of models of arithmetic.George Mills - 1979 - Annals of Mathematical Logic 16 (2):145.

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