elementarily equivalent


All structuresMathworldPlanetmath share a common signaturePlanetmathPlanetmathPlanetmath; the first-order language L is the languagePlanetmathPlanetmath determined by that signature.


The theory of a structure MTh(M), is the set of all sentencesMathworldPlanetmath of L that are true in M.


Structures M and N are elementarily equivalent, (in symbols: MN) if and only if Th(M)=Th(N).

Title elementarily equivalent
Canonical name ElementarilyEquivalent
Date of creation 2013-03-22 13:00:26
Last modified on 2013-03-22 13:00:26
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 8
Author CWoo (3771)
Entry type Definition
Classification msc 03C99
Defines theory