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On the relation between elementary partial difference equations and partial differential equations

I. P. van den Berg

Annals of Pure and Applied Logic 92 (3):235-265 (1998)

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Extended use of IST.I. P. Van den Berg - 1992 - Annals of Pure and Applied Logic 58 (1):73-92.details Van den Berg, I.P., Extended use of IST, Annals of Pure and Applied Logic 58 73–92. Internal Set Theory is an axiomatic approach to nonstandard analysis, consisting of three axiom schemes, Transfer , Idealization , and Standardization . We show that the range of application of these axiom schemes may be enlarged with respect to the original formulation. Not only more kinds of formulas are allowed, but also different settings. Many examples illustrate these extensions. Most concern formal aspects of nonstandard (...) asymptotics. (shrink) Download Export citation Bookmark 6 citations
From discrete to continuous time.H. Jerome Keisler - 1991 - Annals of Pure and Applied Logic 52 (1-2):99-141.details A general metatheorem is proved which reduces a wide class of statements about continuous time stochastic processes to statements about discrete time processes. We introduce a strong language for stochastic processes, and a concept of forcing for sequences of discrete time processes. The main theorem states that a sentence in the language is true if and only if it is forced. Although the stochastic process case is emphasized in order to motivate the results, they apply to a wider class of (...) Download Export citation Bookmark 4 citations
Nonstandard Measure Theory and its Applications.Nigel J. Cutland - 1983 - Journal of Symbolic Logic 54 (1):290-291.details Download Export citation Bookmark 13 citations

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