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Forking in Generic Structures(Study of definability in nonstandard models of arithmetic)

Forking in Generic Structures(Study of definability in nonstandard models of arithmetic)
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Weakly o-minimal structures(Study of definability in nonstandard models of arithmetic)

Weakly o-minimal structures(Study of definability in nonstandard models of arithmetic)
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On weak determinacy of infinite binary games(Study of definability in nonstandard models of arithmetic)

On weak determinacy of infinite binary games(Study of definability in nonstandard models of arithmetic)
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On P-closure operator in quasi-minimal structures(Study of definability in nonstandard models of arithmetic)

On P-closure operator in quasi-minimal structures(Study of definability in nonstandard models of arithmetic)
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Quantifier elimination of the products of ordered abelian groups(Study of definability in nonstandard models of arithmetic)

Quantifier elimination of the products of ordered abelian groups(Study of definability in nonstandard models of arithmetic)
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Nonstandard models that are definable in models of Peano Arithmetic

Mathematical Logic Quarterly, 2007
AbstractIn this paper, we investigate definable models of Peano Arithmetic PA in a model of PA. For any definable model N without parameters in a model M, we show that N is isomorphic to M if M is elementary extension of the standard model and N is elementarily equivalent to M.
Ikeda, Kazuma, Tsuboi, Akito
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Lectures on Nonstandard Models of Arithmetic

Studies in Logic and the Foundations of Mathematics, 1984
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Amalgamation of nonstandard models of arithmetic

Journal of Symbolic Logic, 1977
AbstractAny two models of arithmetic can be jointly embedded in a third with any prescribed isomorphic submodels as intersection and any prescribed relative ordering of the skies above the intersection. Corollaries include some known and some new theorems about ultrafilters on the natural numbers, for example that every ultrafilter with the “4 to 3 ...
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Recursively saturated nonstandard models of arithmetic

Journal of Symbolic Logic, 1981
Through the ability of arithmetic to partially define truth and the ability of infinite integers to simulate limit processes, nonstandard models of arithmetic automatically have a certain amount of saturation: Any encodable partial type whose formulae all fall into the domain of applicability of a truth definition must, by finite satisfiability and ...
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Addition in nonstandard models of arithmetic

Journal of Symbolic Logic, 1972
In [3] Kemeny made the following conjecture: Suppose *Z is a nonstandard model of the ring of integers Z. Letand let F be the subgroup of those cosets ā which contain an element of infinite height in *Z. Kemeny then asked if the ring R = {a: ā ∈ F} is also a nonstandard model of Z. If so then Goldbach's conjecture is false because Kemeny also shows in [
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