Name
Abstract | ||
|---|---|---|
An uncountable cardinal kappa is called (1)-strongly compact if every kappa-complete ultrafilter on any set I can be extended to an omega(1)-complete ultrafilter on I. We show that the first omega(1)-strongly compact cardinal, kappa(0), cannot be a successor cardinal, and that its cofinality is at least the first measurable cardinal. We prove that the Singular Cardinal Hypothesis holds above kappa(0). We show that the product of Lindel of spaces is kappa-Lindel of if and only if kappa >= kappa(0). Finally, we characterize kappa(0) in terms of second order reflection for relational structures and we give some applications. For instance, we show that every first-countable nonmetrizable space has a nonmetrizable subspace of size less than kappa(0). |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1017/jsl.2013.12 | JOURNAL OF SYMBOLIC LOGIC |
Keywords | DocType | Volume |
omega(1)-strongly compact cardinal,Singular Cardinal Hypothesis,Lindelof space,second-order reflection,countably chromatic graph,metrizable space,completely regular space | Journal | 79 |
Issue | ISSN | Citations |
1 | 0022-4812 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Joan Bagaria | 1 | 63 | 13.15 |
| Menachem Magidor | 2 | 1369 | 140.76 |