Arithmetic | Model theory | Mathematical logic | Formal theories of arithmetic

Non-standard model of arithmetic

In mathematical logic, a non-standard model of arithmetic is a model of (first-order) Peano arithmetic that contains non-standard numbers. The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non-standard model is one that has additional elements outside this initial segment. The construction of such models is due to Thoralf Skolem (1934). (Wikipedia).

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Follow-up video: https://youtu.be/7HKnOOvssvs Discussed text, including all links: https://gist.github.com/Nikolaj-K/101c2712dc832dec4991bf568869abc8 Curt's call: https://youtu.be/V93GQaDtv8w Timestamps: 00:00:00 Introduction 00:02:55 Wittgenstein and predicates (optional) 00:11:12 Skolems

From playlist Logic

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From playlist Math Foundations

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From playlist Modern linear algebra using Python instead of a textbook

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From playlist Linear Algebra (Full Course)

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From playlist Foundations seminar

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From playlist Zermelo Fraenkel axioms

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From playlist Mathematics

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Related pages

Tennenbaum's theorem | Gödel's incompleteness theorems | Löwenheim–Skolem theorem | Total order | Peano axioms | Compactness theorem | Zermelo–Fraenkel set theory | Order type | Second-order logic | Approximations of π | Dense order | Mathematical logic | Semiring | Gödel's completeness theorem | Ultraproduct | Thoralf Skolem | Cardinality | Goodstein's theorem | First-order logic