If L is a logical language for some logic , a set T of formulasMathworldPlanetmath with no free variablesMathworldPlanetmathPlanetmath is called a theory (of ). If is a first-order logic, then T is called a first-order theory.

We write Tϕ for any formula ϕ if every model of such that MT, Mϕ.

We write Tϕ is for there is a proof of ϕ from T.

Remark. Let S be an L-structureMathworldPlanetmath for some signaturePlanetmathPlanetmathPlanetmath L. The theory of S is the set of formulas satisfied by S:


and is denoted by Th(S).

Title theory
Canonical name Theory
Date of creation 2013-03-22 13:00:12
Last modified on 2013-03-22 13:00:12
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 8
Author CWoo (3771)
Entry type Definition
Classification msc 03B10
Classification msc 03B05