P-points and Q-points over a measurable cardinal |
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Authors: | C Sureson |
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Institution: | Dept. of Mathematics, Graduate Center of CUNY, 33 W 42 Street, New York, NY 10036, USA |
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Abstract: | This paper presents constructions of κ-ultrafilters over a measurable cardinal κ, specifically p-points and q-points, in the continuation of works of Gitik, Kanamori and Ketonen. On the assumption of supercompactness, Kunen has shown the existence of a chain of p-points, in the Rudin–Keisler ordering, of maximal length. We shall prove a similar result for q-points. Results of Mitchell 8,9] establish connections between Rudin—Keisler chains of κ-ultrafilters and inner models of “?ν(o(ν)= ν++)”. This shows the necessity of some strong large cardinal hypothesis. The second part of the paper is devoted to a separation property of κ- ultrafilters (cf. Kanamori and Taylor). To answer a question of Taylor concerning the existence of a non-separating p-point, we use a combination of Silver's Forcing and iterated ultrapowers; the proof itself may be of some interest. |
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