combinatorial principle

A combinatorial principle is any statement Φ of set theoryMathworldPlanetmath proved to be independent of Zermelo-Fraenkel (ZF) set theory, usually one with interesting consequences.

If Φ is a combinatorial principle, then whenever we have implicationsMathworldPlanetmath of the form


we automatically know that P is unprovable in ZF and Q is relatively consistent with ZF.

Some examples of combinatorial principles are the axiom of choiceMathworldPlanetmath (, the continuum hypothesisMathworldPlanetmath, , , and Martin’s axiom.


  • 1 Just, W., just/resint.html#principles
Title combinatorial principle
Canonical name CombinatorialPrinciple
Date of creation 2013-03-22 14:17:41
Last modified on 2013-03-22 14:17:41
Owner mps (409)
Last modified by mps (409)
Numerical id 6
Author mps (409)
Entry type Definition
Classification msc 03E65
Related topic DiamondMathworldPlanetmath
Related topic Clubsuit