Name
Abstract | ||
|---|---|---|
1 )+, then there is no precipitous ideal on ω1. We show that a collapsing function for ω2 can be added by forcing. We define what it means to be a weakly ω1-Erdos cardinal and show that in L(E), there is a collapsing function for λ iff λ is less than the least weakly ω1-Erdos cardinal. As a corollary to our results and a theorem of Neeman, the existence of a Woodin limit of Woodin cardinals does not imply the existence of precipitous ideals on ω1. We also show that the following statements hold in L(E). The least cardinal λ with the Chang property (λ, ω1) (ω1 ,ω ) is equal to the least ω1-Erdos cardinal. In particular, if j is a generic elementary embedding that arises from non-stationary tower forcing up to a Woodin cardinal, then the minimum possible value of j(ω1) is the least ω1-Erdos cardinal. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1002/malq.200310069 | Math. Log. Q. |
Keywords | DocType | Volume |
large cardinal,precipitous ideal,core model. msc 2000 03e55 | Journal | 50 |
Issue | Citations | PageRank |
1 | 3 | 0.73 |
References | Authors | |
1 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ernest Schimmerling | 1 | 3 | 0.73 |
| Boban Velickovic | 2 | 47 | 6.80 |