Results 261 to 270 of about 19,658 (300)

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.
Kazuma Ikeda, Akito Tsuboi
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Nonstandard natural number systems and nonstandard models

Journal of Symbolic Logic, 1981
AbstractIt is known (see [1, 3.1.5]) that the order type of the nonstandard natural number system *N has the form ω + (ω* + ω) θ, where θ is a dense order type without first or last element and ω is the order type of N. Concerning this, Zakon [2] examined *N more closely and investigated the nonstandard real number system *R, as an ordered set, as an ...
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A nonstandard model

Foundations of Physics, 1993
An elementary-particle picture developed primarily by Barut as an alternative to the standard model is re-examined. This model is formulated on the basis of strong short-range magnetic interactions among the stable particles (p, e−, v) and at present is able to account qualitatively for most of the known phenomena.
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On nonstandard models in higher order logic

Journal of Symbolic Logic, 1984
There are two concepts of standard/nonstandard models in simple type theory.The first concept—we might call it the pragmatical one—interprets type theory as a first order logic with countably many sorts of variables: the variables for the urelements of type 0,…, the n-ary relational variables of type (τ1, …, τn) with arguments of type (τ1,…,τn ...
Christian Hort, Horst Osswald
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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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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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Nonstandard model of the expanding universe

International Journal of Theoretical Physics, 1992
A reformulation of general relativity is proposed with the relativity principle being invalid. Consequently the space-time manifold carries a natural (1+3)-foliation, where the foliation variables supersede the metric as the fundamental object. The Einstein equations become modified by some kind of foliation energy, but otherwise remain part of the ...
M. Mattes, M. Sorg
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Special Model Axiom in Nonstandard Set Theory

Mathematical Logic Quarterly, 1999
AbstractWe demonstrate that the special model axiom SMA of Ross admits a natural formalization in Kawai's nonstandard set theory KST but is independent of KST. As an application of our methods to classical model theory, we present a short proof of the consistency (with ZFC) of the existence of a k+ like k‐saturated model of PA for a given cardinal k.
Vladimir Kanovei, Michael Reeken
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The special model axiom in nonstandard analysis

Journal of Symbolic Logic, 1990
κ-saturation [SL] is probably the single most useful property of nonstandard models of analysis. For some applications, however, stronger saturation hypotheses seem necessary. Henson formulated his elegant κ-isomorphism property (see [H1], and §2 below) to address this need. This property, though well-suited to certain situations (notably those arising
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