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Using the core model K we determine better lower bounds for the consistency strength of some combinatorial principles: I. Assume that A is a Jonsson cardinal which is 'accessible' in the sense that at least one of (l)-(4) holds: (1) A is a successor cardinal; (2) A = oE and 6 <A ; (3) A is singular of uncountable cofinality; (4) A is a regular but not… (More)

- Florian Rudolph, Hans-Dieter Donder, Ronald B. Jensen, Matthew Foreman, Menachem Magidor, Saharon Shelah
- 2000

An ultraalter V on some regular cardinal is called ()-regular ii there is a sequence ha j < i of elements of V such that the intersection of any-many of them is empty. V is regular ii it is (!!)-regular. Regular ultraalters were rst considered in Model Theory, where Keisler showed that they yield ultrapowers of maximal cardinality. The proof of the… (More)

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