Concept

# Lindström quantifier

Summary
In mathematical logic, a Lindström quantifier is a generalized polyadic quantifier. Lindström quantifiers generalize first-order quantifiers, such as the existential quantifier, the universal quantifier, and the counting quantifiers. They were introduced by Per Lindström in 1966. They were later studied for their applications in logic in computer science and database query languages. Generalization of first-order quantifiers In order to facilitate discussion, some notational conventions need explaining. The expression : \phi^{A,x,\bar{a}}={x\in A\colon A\models\phi[x,\bar{a}]} for A an L-structure (or L-model) in a language L, φ an L-formula, and \bar{a} a tuple of elements of the domain dom(A) of A. In other words, \phi^{A,x,\bar{a}} denotes a (monadic) property defined on dom(A). In general, where x is replaced by an n-tuple \bar{x} of free variables, \phi^{A,\bar{x},\bar{a}} denotes an n-ary rela
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