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 lambda-Archimedean ultrapowers of omega under some large cardinal assumptions. For example, we show that, assuming the consistency of a measurable cardinal, there may exist a lambda-Archimedean ultrapower of omega for some uncountable cardinal lambda. This answers a question in [KS], modulo the assumption of measurability.
Keywords
Cite
@article{arxiv.math/9801153,
title = {Possible Size of an ultrapower of omega},
author = {Renling Jin and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9801153},
year = {2009}
}