combinatorial principle
A combinatorial principle is any statement Φ of set theory 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 implications
of the form
P⟹Φ⟹Q, |
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 choice (http://planetmath.org/AxiomOfChoice), the continuum hypothesis
, ◇, ♣, and Martin’s axiom.
References
- 1 Just, W., http://www.math.ohiou.edu/ just/resint.html#principleshttp://www.math.ohiou.edu/~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 | Diamond![]() |
Related topic | Clubsuit |