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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Topology and Set Theory Seminar


Shelah's proof of diamond

Prelegent: Jakub Andruszkiewicz

2021-05-05 16:15

It is a well-known fact that the diamond principle implies CH, but the reverse implication does not hold. The situation for successor cardinals larger than the first uncountable cardinal is quite different - as proved by Shelah, if only cardinal kappa is uncountable, then 2^kappa = kappa^+ is enough for a majority of possible natural generalizations of the diamond principle on kappa^+ to hold. During the talk the P. Komjath's formulation of the above mentioned proof by Shelah, included in the article "Shelah's proof of diamond", will be presented.