Preservation of measurability and forcing

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R. Honzik (logic seminar 19. and 26.2.2007)

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Abstract:

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.