Possible size of an ultrapower of \omega |
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| Authors: | Renling Jin Saharon Shelah |
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| Institution: | (1) Department of Mathematics, College of Charleston, Charleston, SC 29424, USA. e-mail: jin@math.cofc.edu , US;(2) Institute of Mathematics, The Hebrew University, Jerusalem, Israel , IL;(3) Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA , US;(4) Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA , US |
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| Abstract: | Let be the first infinite ordinal (or the set of all natural numbers) with the usual order . In § 1 we show that, assuming the consistency of a supercompact cardinal, there may exist an ultrapower of , whose cardinality is (1) a singular strong limit cardinal, (2) a strongly inaccessible cardinal. This answers two questions
in 1], modulo the assumption of supercompactness. In § 2 we construct several -Archimedean ultrapowers of under some large cardinal assumptions. For example, we show that, assuming the consistency of a measurable cardinal, there
may exist a -Archimedean ultrapower of for some uncountable cardinal . This answers a question in 8], modulo the assumption of measurability.
Received: 19 November 1996 |
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| Keywords: | Mathematics Subject Classification (1991):Primary 03C20 03E35 03E55 03G05 Secondary 03C62 03H15 |
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