Nonstandard methods and applications in mathematics
Association for Symbolic Logic, 2006 - Mathematics - 248 pages
A conference on Nonstandard Methods and Applications in Mathematics (NS2002) was held in Pisa, Italy from June 12-16, 2002. Nonstandard analysis is one of the great achievements of modern applied mathematical logic. In addition to the important philosophical achievement of providing a sound mathematical basis for using infinitesimals in analysis, the methodology is now well established as a tool for both research and teaching, and has become a fruitful field of investigation in its own right. This book is a collection of peer-reviewed papers solicited from some of the participants of this conference with the aim of providing something more timely than a textbook, but less ephemeral than a conventional proceedings. It contains both survey papers and research articles with special consideration for one, "Nonstandard analysis at pre-university level: naive magnitude analysis" in which the author discusses his experience teaching calculus through an infinitesimal approach.
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Vieri Benci Mauro Di Nasso and Marco Forti
Sergio Fajardo and H Jerome Keisler
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algebraic assume attractor axiomatic axioms bounded cardinal closed formula cohomology condition consecutive numbers construction crowded triple Cutland defined Definition density e-formula elementary elements equivalent etale etale cohomology example exists external sets external universe finite Forcing Theorem function functor Galerkin approximation Hausdorff Hence hyper-extensions hyper-methods hyperfinite hyperreal induction infinite infinitesimal Internal set theory internal sets intersection isomorphic Kanovei Keisler Lemma Loeb measures Loeb space metric space model theory Nash equilibrium Nasso natural numbers Navier-Stokes equations Neoclosed Forcing neoclosed formula neocompact set neocontinuous neoseparable neotight nonempty nonstandard analysis Nonstandard Methods nonstandard set theory notion numbers numerosities presheaf probability space Proposition proved real numbers result satisfies saturation Section sort standard sets stochastic Navier-Stokes equations structure subset subspace superstructure Suppose Symbolic Logic Theorem 3.1 topological extension transfer principle ultrafilter ultrapowers ultraproduct Wiener process