Prelegent: Ziemowit Kostana

Parametrized diamonds are combinatorial principles that imply many consequences of the original Jensen's Diamond, yet are consistent with the CH failing. Informally speaking, they are in similar relation to Jensen's Diamond, as cardinal invariants of the Cichoń's diagram are to CH. The modern framework for these axioms was described by Moore, Hrusak, and Dzamonja. I would like to show that some equivalent, or closely related, axioms can be formulated in a completely different, game-theoretic, language. This gives additional insight on how these axioms affect the set theoretic universe.