On the strong equality between supercompactness and strong compactness
Arthur W. Apter and Saharon Shelah
Trans. Amer. Math. Soc. 349 (1997), 103-128
Primary 03E35; Secondary 03E55.
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Abstract: We show that supercompactness and strong compactness can be equivalent even as properties of pairs of regular cardinals. Specifically, we show that if ZFC + GCH is a given model (which in interesting cases contains instances of supercompactness), then there is some cardinal and cofinality preserving generic extension ZFC + GCH in which, (a) (preservation) for regular, if is supercompact'', then is supercompact'' and so that, (b) (equivalence) for regular, is strongly compact'' iff is supercompact'', except possibly if is a measurable limit of cardinals which are supercompact.
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Arthur W. Apter
Department of Mathematics, Baruch College of CUNY, New York, New York 10010
Department of Mathematics, The Hebrew University, Jerusalem, Israel;
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08904
Strongly compact cardinal,
Received by editor(s):
May 2, 1994
Received by editor(s) in revised form:
December 30, 1994
The research of the first author was partially supported by PSC-CUNY Grant 662341 and a salary grant from Tel Aviv University. In addition, the first author wishes to thank the Mathematics Departments of The Hebrew University and Tel Aviv University for the hospitality shown him during his sabbatical in Israel. The second author wishes to thank the Basic Research Fund of the Israeli Academy of Sciences for partially supporting this research, which is Publication 495 of the second author.
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