| Time: | 12:00 - 13:20 |
| Room: |
Doherty Hall 4303
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| Speaker: |
James Cummings Department of Mathematical Sciences Carnegie Mellon University |
| Title: |
The Generalised Continuum Hypothesis and Jensen's diamond principle.
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| Abstract: | The generalised continuum hypothesis (GCH) is the assertion that for every infinite cardinal kappa, the powerset of kappa has the least possible size (kappa-plus). Jensen's diamond principle (diamond at kappa-plus) is a strengthening of this assertion which is often useful in building objects of size kappa-plus (trees, graphs, colourings, models). Recently Shelah proved that for uncountable kappa these assertions are actually equivalent; I'll give some history and then sketch Shelah's proof. |