Model Theory of Nonstandard Structures with Applications

Roman Kossak ()
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Roman Kossak: CUNY, The Graduate Center

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 1921-1931 from Springer

Abstract: Abstract Every infinite mathematical structure M $$ \mathcal{M} $$ has an extension M ∗ $$ {\mathcal{M}}^{\ast } $$ that has the same first-order properties as M $$ \mathcal{M} $$ , but is not isomorphic to M $$ \mathcal{M} $$ . In this sense, M ∗ $$ {\mathcal{M}}^{\ast } $$ can be considered a nonstandard extension of M $$ \mathcal{M} $$ . A short discussion of the idea of nonstandard models is followed by proofs of three easy standard results that use nonstandard extensions in essential ways. The aim is to explain basic model-theoretic concepts behind such proofs.

Keywords: Model theory; First-order logic; Nonstandard models; Automorphisms (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-40846-5_71

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DOI: 10.1007/978-3-031-40846-5_71

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