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  • CHANG’S CONJECTURE, GENERIC ELEMENTARY EMBEDDINGS AND INNER MODELS FOR HUGE CARDINALS

  • MATTHEW FOREMAN
  • Journal:
    Bulletin of Symbolic Logic / Volume 21 / Issue 3 / September 2015
    Published online by Cambridge University Press:
    15 September 2015, pp. 251-269
    Print publication:
    September 2015

  • We introduce a natural principle Strong Chang Reflection strengthening the classical Chang Conjectures. This principle is between a huge and a two huge cardinal in consistency strength. In this note we prove that it implies the existence of an inner model with a huge cardinal. The technique we explore for building inner models with huge cardinals adapts to show that decisive ideals imply the existence of inner models with supercompact cardinals. Proofs for all of these claims can be found in [10].1,2