quantifier free


Let L be a first order language. A formulaMathworldPlanetmath ψ is quantifier free iff it contains no quantifiersMathworldPlanetmath.

Let T be a completePlanetmathPlanetmathPlanetmathPlanetmathPlanetmath L-theory. Let SL. Then S is an elimination set for T iff for every ψ(x¯)L there is some ϕ(x¯)S so that Tx¯(ψ(x¯))ϕ(x¯).

In particular, T has quantifier elimination iff the set of quantifier free formulas is an elimination set for T. In other T has quantifier elimination iff for every ψ(x¯)L there is some quantifier free ϕ(x¯)L so that Tx¯(ψ(x¯))ϕ(x¯).

Title quantifier free
Canonical name QuantifierFree
Date of creation 2013-03-22 13:27:49
Last modified on 2013-03-22 13:27:49
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 7
Author mathcam (2727)
Entry type Definition
Classification msc 03C10
Classification msc 03C07
Classification msc 03B10
Related topic Quantifier
Related topic LogicalLanguage
Defines quantifier free formula
Defines quantifier elimination
Defines elimination set