A new condensation principle |
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| Authors: | Thoralf Räsch Ralf Schindler |
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| Affiliation: | (1) Institut für Mathematik, Universität Potsdam, Postfach 60 15 53, 14415 Potsdam, Germany;(2) Institut für mathematische Logik und Grundlagenforschung, Westfälische Wilhelms–Universität Münster, Einsteinstraße 62, 48149 Münster, Germany |
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| Abstract: | We generalize  (A), which was introduced in [Sch ], to larger cardinals. For a regular cardinal  > 0 we denote by (A) the statement that  and for all regular  >, is stationary in  It was shown in [Sch] that  can hold in a set-generic extension of L. We here prove that  can hold in a set-generic extension of L as well. In both cases we in fact get equiconsistency theorems. This strengthens results of [Rä00] and [Rä01].  is equivalent with the existence of 0#.Mathematics Subject Classification (1991): Primary 03E55, 03E15, Secondary 03E35, 03E60 |
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| Keywords: | Set theory Proper forcing Large cardinals |
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