ultraproduct
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Ultraproduct — An ultraproduct is a mathematical construction, of which the ultrapower (defined below) is a special case. Ultraproducts are used in abstract algebra to construct new fields from given ones, and in model theory, a branch of mathematical logic. In … Wikipedia
metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… … Universalium
Ax–Kochen theorem — The Ax–Kochen theorem, named for James Ax and Simon B. Kochen, states that for each positive integer d there is a finite set Yd of prime numbers, such that if p is any prime not in Yd then every homogeneous polynomial of degree d over the p adic… … Wikipedia
Non-standard model of arithmetic — In mathematical logic, a nonstandard model of arithmetic is a model of (first order) Peano arithmetic that contains nonstandard numbers. The standard model of arithmetic consists of the set of standard natural numbers {0, 1, 2, …}. The elements… … Wikipedia
Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it … Wikipedia
Ultrafilter — In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged (as a filter). An ultrafilter may be considered as a finitely additive measure. Then every subset of X is … Wikipedia
Compactness theorem — In mathematical logic, the compactness theorem states that a set of first order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory, as it provides a useful method for… … Wikipedia
Jerzy Łoś — c.1955 Jerzy Łoś (born March 22, 1920 in Lwów (now Lviv, Ukraine) June 1, 1998 in Warsaw) (Polish pronunciation: [ˈjɛʐɨ ˈwɔɕ]) was a Polish mathematician, logician, economist, and philosopher. He is best known for his work on ultraproducts,… … Wikipedia
Cartesian product — Cartesian square redirects here. For Cartesian squares in category theory, see Cartesian square (category theory). In mathematics, a Cartesian product (or product set) is a construction to build a new set out of a number of given sets. Each… … Wikipedia
Reduction — Reduction, reduced, or reduce may refer to:cienceChemistry*Reduction – chemical reaction in which atoms have their oxidation number (oxidation state) changed. **Reduced gas – a gas with a low oxidation number **Ore reduction: see… … Wikipedia
