Preservation of measurability and forcing

R. Honzik (logic seminar 19. and 26.2.2007)


We shall review some of the techniques used to lift elementary embeddings to generic extensions. By way of example we show the Woodin's proof that if \kappa is \kappa+2-strong cardinal, then there is a generic extension where \kappa is still measurable and 2^\kappa = \kappa^{++}. We will discuss some generalizations of Woodin's proof to include other and more complex forcing notions.