universal relation


If Φ is a class of n-ary relationsMathworldPlanetmath with x as the only free variablesMathworldPlanetmathPlanetmath, an n+1-ary formulaMathworldPlanetmathPlanetmath ψ is universalPlanetmathPlanetmath for Φ if for any ϕΦ there is some e such that ψ(e,x)ϕ(x). In other words, ψ can simulate any element of Φ.

Similarly, if Φ is a class of function of x, a formula ψ is universal for Φ if for any ϕΦ there is some e such that ψ(e,x)=ϕ(x).

Title universal relation
Canonical name UniversalRelation
Date of creation 2013-03-22 12:58:18
Last modified on 2013-03-22 12:58:18
Owner Henry (455)
Last modified by Henry (455)
Numerical id 6
Author Henry (455)
Entry type Definition
Classification msc 03B10
Synonym universal
Defines universal function