The nonstationary ideal on ℵ2
We construct a model in which the filter of ω-closed unbounded subsets of ℵ2 is precipitous and a model in which the filter of closed unbounded subsets of ℵ2 is precipitous. For the first model we need a measurable cardinal, and for the second a measurable cardinal of order 2. Both results are equiconsistent.
KeywordsDense Subset Generic Subset Measurable Cardinal Force Notion Elementary Chain
Unable to display preview. Download preview PDF.
- 4.K. J. Devlin,Indescribability properties and small large cardinals, inLogic Conference, Kiel 1974, Lecture Notes in Math.499, Springer, Berlin, 1975, pp. 89–117.Google Scholar
- 6.T. Jech,Set Theory, Academic Press, 1978.Google Scholar
- 10.A. Lévy,The sizes of the indescribable cardinals, inAxiomatic Set Theory (D. S. Scott, ed.), Proc. Symp. Pure Math.13 (1), Am. Math. Soc., Providence, RI, 1971, pp. 205–218.Google Scholar
- 11.W. Mitchell,The core model for sequences of measures, to appear.Google Scholar
- 12.S. Shelah,Iterated forcing and changing cofinalities, Isr. J. Math,40 (1981), 1–32.Google Scholar
- 13.S. Shelah,Iterated Forcing and Changing Cofinalities II, preprint.Google Scholar
- 15.T. Jech,Stationary subsets of inaccessible cardinals, to appear.Google Scholar