Possible Size of an ultrapower of omega
Abstract
Let omega be the first infinite ordinal (or the set of all natural numbers) with the usual order <. In section 1 we show that, assuming the consistency of a supercompact cardinal, there may exist an ultrapower of omega, whose cardinality is (1) a singular strong limit cardinal, (2) a strongly inaccessible cardinal. This answers two questions in [CK], modulo the assumption of supercompactness. In section 2 we construct several lambdaArchimedean ultrapowers of omega under some large cardinal assumptions. For example, we show that, assuming the consistency of a measurable cardinal, there may exist a lambdaArchimedean ultrapower of omega for some uncountable cardinal lambda. This answers a question in [KS], modulo the assumption of measurability.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 1998
 DOI:
 10.48550/arXiv.math/9801153
 arXiv:
 arXiv:math/9801153
 Bibcode:
 1998math......1153J
 Keywords:

 Mathematics  Logic