2002/12/01 by W. Hugh Woodin
Mathematics · #math.LO #msc:03E45 #msc:03E55 #msc:03E10 #msc:04A10 #msc:04A13
published as Proceedings of the ICM, Beijing 2002, vol. 1, 515--524
arxiv created 2002/12/01 · arxiv updated 2009/12/01
There have been many generalizations of Shoenfield's Theorem on the absoluteness of Σ12 sentences between uncountable transitive models of ZFC. One of the strongest versions currently known deals with Σ21 absoluteness conditioned on CH. For a variety of reasons, from the study of inner models and from simply combinatorial set theory, the question of whether conditional Σ22 absoluteness is possible at all, and if so, what large cardinal assumptions are involved and what sentence(s) might play the role of CH, are fundamental questions. This article investigates the possiblities for Σ22 absoluteness by extending the connections between determinacy hypotheses and absoluteness hypotheses.