The Core Model Iterability ProblemLarge cardinal hypotheses play a central role in modern set theory. One important way to understand such hypotheses is to construct concrete, minimal universes, or "core models", satisfying them. Since Gödel's pioneering work on the universe of constructible sets, several larger core models satisfying stronger hypotheses have been constructed, and these have proved quite useful. Here the author extends this theory so that it can produce core models satisfying "There is a Woodin cardinal", a large cardinal hypothesis which is the focus of much current research. The book is intended for advanced graduate students and reseachers in set theory. |
Contents
0 Introduction | 1 |
3 Thick classes and universal weasels | 25 |
6 An inductive definition of K | 43 |
Copyright | |
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Common terms and phrases
1-iterable 1-small a-good a-strong a+)K Ao-thick assume canonical embedding claim coarse premouse cofinal wellfounded branch completes the proof construction contradiction core model countable crit crit(j critical point cutoff points Def(K Def(W elementary submodel exists extender derived follows FSIT fully elementary hull property identity implies inaccessible initial segment inner model iterable weasel iteration map iteration strategy JK is Ao-sound k-maximal last model length limit ordinal linear iteration measurable cardinal moreover normal iteration tree normal measure phalanx premice proper class proper premouse properly small Qi+1 realization resurrection S-hull S-sound S-thick strong cardinal strongly compact cardinal successful coiteration successor cardinal Suppose Kc Theorem thick transitive collapse transitive set Ult(N Ult(W ultrapower unique universal weasel V-generic V₁ w₁ witnesses that JK Woodin cardinals α α