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Reals constructible from many countable sets of ordinals (2005).
| Content Provider | CiteSeerX |
|---|---|
| Author | Larson, Paul B. |
| Abstract | We show that if there exist proper class many Woodin cardinals, then the set of reals x for which there is exists an ordinal α with {a ∈ Pω1(α) x ∈ L[a]} stationary is countable. These results were announced in [2]. Given a real x and an ordinal α, we let C(x, α) denote the set {a ∈ Pω1(α) x ∈ L[a]}. We let C denote the set of reals x for which there exists an ordinal α such that C(x, α) is club. We assume some familiarity with the stationary tower Q<δ (see [2]). Theorem 0.1. Suppose that there exists a proper class of Woodin cardinals. Then for every real x and every ordinal α, C(x, α) is either club or nonstation-ary, and C is countable. Proof. Fix a cardinal λ such that, for every real x, • if there exists an ordinal α with C(x, α) stationary and costationary, then there is such an ordinal below λ, |
| File Format | |
| Publisher Date | 2005-01-01 |
| Access Restriction | Open |
| Subject Keyword | Many Countable Set Class Many Woodin Cardinal Stationary Tower Proper Class Woodin Cardinal |
| Content Type | Text |
