Results 261 to 270 of about 6,651,187 (298)

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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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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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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A recursive nonstandard model of normal open induction

Journal of Symbolic Logic, 1996
AbstractModels of normal open induction are those normal discretely ordered rings whose nonnegative part satisfy Peano's axioms for open formulas in the language of ordered semirings. (Where normal means integrally closed in its fraction field.)In 1964 Shepherdson gave a recursive nonstandard model of open induction.
Alessandro Berarducci, Margarita Otero
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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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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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NONSTANDARD MODELS IN RECURSION THEORY AND REVERSE MATHEMATICS

The Bulletin of Symbolic Logic, 2014
AbstractWe give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models, and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic.
Li, Wei, Chong, Chi Tat, Yang, Yue
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The nonstandard λ:φ24(x): model. II. The standard model from a nonstandard point of view

Journal of Mathematical Physics, 1972
As a second step in the construction of the nonstandard λ:φ24: model we analyze Glimm and Jaffe's work from the nonstandard point of view.
Peter J. Kelemen, Abraham Robinson
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