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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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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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The intersection of nonstandard models of arithmetic

Journal of Symbolic Logic, 1972
If two nonstandard models of complete arithmetic are elementarily embedded in a third, then their intersection may be considerably smaller than either of them; indeed, the intersection may be only the standard model. For example, if D and E are nonprincipal ultrafilters on ω, then the nonstandard models D-prod and E-prod (where is the standard model)
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Recursively saturated nonstandard models of arithmetic; addendum

Journal of Symbolic Logic, 1982
These additions to the author's paper [ibid. 46, 259-286 (1981; Zbl 0501.03044)] rely mainly on unpublished work of several authors. In particular, an argument (due to R. Solovay) is outlined that there are no short cofinally resplendent models.
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On external Scott algebras in nonstandard models of Peano arithmetic

Journal of Symbolic Logic, 1996
AbstractWe prove that a necessary and sufficient condition for a countable set of sets of integers to be equal to the algebra of all sets of integers definable in a nonstandard elementary extension of ω by a formula of the PA language which may include the standardness predicate but does not contain nonstandard parameters, is as follows: is closed ...
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