Definition 1.
Let be a stationary set. Then the combinatorial principle holds if and only if there is a sequence such that each and for any , is stationary.
To get some sense of what this means, observe that for any , , so the set of is stationary (in ). More strongly, suppose . Then any subset of is bounded in so on a stationary set. Since , it follows that . Hence , the most common form (often written as just ), implies CH.
C. Akemann and N. Weaver used to construct a -algebra serving as a counterexample to Naimark’s problem.
References
- 1 Akemann, C., and N. Weaver, Consistency of a counterexample to Naimark’s problem. Preprint available on the arXiv at http://arxiv.org/abs/math.OA/0312135http://arxiv.org/abs/math.OA/0312135.
Title | |
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Canonical name | Diamond |
Date of creation | 2013-03-22 12:53:49 |
Last modified on | 2013-03-22 12:53:49 |
Owner | Henry (455) |
Last modified by | Henry (455) |
Numerical id | 8 |
Author | Henry (455) |
Entry type | Definition |
Classification | msc 03E65 |
Synonym | diamond |
Related topic | Clubsuit |
Related topic | DiamondIsEquivalentToClubsuitAndContinuumHypothesis |
Related topic | ProofOfDiamondIsEquivalentToClubsuitAndContinuumHypothesis |
Related topic | CombinatorialPrinciple |
Defines |