combinatorial principle
A combinatorial principle is any statement of set theory proved to be independent of Zermelo-Fraenkel (ZF) set theory, usually one with interesting consequences.
If is a combinatorial principle, then whenever we have implications of the form
we automatically know that is unprovable in ZF and 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 |