Prelegent: Jakub Andruszkiewicz

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.