definable formula
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Definable set — In mathematical logic, a definable set is an n ary relation on the domain of a structure whose elements are precisely those elements satisfying some formula in the language of that structure. A set can be defined with or without parameters, which … Wikipedia
Definable real number — A real number a is first order definable in the language of set theory, without parameters, if there is a formula φ in the language of set theory, with one free variable, such that a is the unique real number such that φ(a) holds in the standard… … Wikipedia
Ordinal definable set — In mathematical set theory, a set S is said to be ordinal definable if, informally, it can be defined in terms of a finite number of ordinals by a first order formula. Ordinal definable sets were introduced by Gödel (1965). A drawback to this… … Wikipedia
Sahlqvist formula — In modal logic, Sahlqvist formulae are a certain kind of modal formula with remarkable properties. The Sahlqvist correspondence theorem states that everySahlqvist formula is canonical,and corresponds to a first order definable class of Kripke… … Wikipedia
Arithmetical hierarchy — In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene hierarchy classifies certain sets based on the complexity of formulas that define them. Any set that receives a classification is called arithmetical. The… … Wikipedia
Structure (mathematical logic) — In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations which are defined on it. Universal algebra studies structures that generalize the algebraic structures such as… … Wikipedia
Constructible universe — Gödel universe redirects here. For Kurt Gödel s cosmological solution to the Einstein field equations, see Gödel metric. In mathematics, the constructible universe (or Gödel s constructible universe), denoted L, is a particular class of sets… … Wikipedia
Arithmetical set — In mathematical logic, an arithmetical set (or arithmetic set) is a set of natural numbers that can be defined by a formula of first order Peano arithmetic. The arithmetical sets are classified by the arithmetical hierarchy.A function f:subseteq… … Wikipedia
Analytical hierarchy — In mathematical logic and descriptive set theory, the analytical hierarchy is a higher type analogue of the arithmetical hierarchy. It thus continues the classification of sets by the formulas that define them. The analytical hierarchy of… … Wikipedia
Second-order logic — In logic and mathematics second order logic is an extension of first order logic, which itself is an extension of propositional logic.[1] Second order logic is in turn extended by higher order logic and type theory. First order logic uses only… … Wikipedia
Interpretable structure — In model theory, a structure N is called interpretable in M if all the components (universe, functions, relations etc.) of N can be defined in terms of the components of M . In particular, the universe of N is represented as a definable subset of … Wikipedia
