If T is a theory of then it is consistent iff there is some model of such that T. If a theory is not consistent then it is inconsistent.

A slightly different definition is sometimes used, that T is consistent iff T⊬ (that is, as long as it does not prove a contradictionMathworldPlanetmathPlanetmath). As long as the proof calculus used is sound and completePlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath, these two definitions are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath.

Title consistent
Canonical name Consistent
Date of creation 2013-03-22 13:00:20
Last modified on 2013-03-22 13:00:20
Owner Henry (455)
Last modified by Henry (455)
Numerical id 6
Author Henry (455)
Entry type Definition
Classification msc 03B99
Defines inconsistent