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algebraically definable

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  • Differentially closed field — In mathematics, a differential field K is differentially closed if every finite system of differential equations with a solution in some differential field extending K already has a solution in K. This concept was introduced by Robinson (1959).… …   Wikipedia

  • Strongly minimal theory — In model theory a branch of mathematical logic a minimal structure is an infinite one sorted structure such that every subset of its domain that is definable with parameters is either finite or cofinite. A strongly minimal theory is a complete… …   Wikipedia

  • Real closed field — In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… …   Wikipedia

  • Stable group — For stable groups in homotopy theory see stable homotopy group or direct limit of groups. In model theory, a stable group is a group that is stable in the sense of stability theory. An important class of examples is provided by groups of finite… …   Wikipedia

  • Model theory — This article is about the mathematical discipline. For the informal notion in other parts of mathematics and science, see Mathematical model. In mathematics, model theory is the study of (classes of) mathematical structures (e.g. groups, fields,… …   Wikipedia

  • List of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …   Wikipedia

  • Stable theory — For differential equations see Stability theory. In model theory, a complete theory is called stable if it does not have too many types. One goal of classification theory is to divide all complete theories into those whose models can be… …   Wikipedia

  • Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …   Wikipedia

  • Type (model theory) — In model theory and related areas of mathematics, a type is a set of first order formulas in a language L with free variables x1, x2,…, xn which are true of a sequence of elements of an L structure . Loosely speaking, types describe possible… …   Wikipedia

  • Logicism — is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic.[1] Bertrand Russell and Alfred North Whitehead… …   Wikipedia

  • Morley rank — In mathematical logic, Morley rank, introduced by Michael D. Morley (1965), is a means of measuring the size of a subset of a model of a theory, generalizing the notion of dimension in algebraic geometry. Contents 1 Definition 2 Examples 3… …   Wikipedia

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