# Sh:626

- Jin, R., & Shelah, S. (1999).
*Possible size of an ultrapower of \omega*. Arch. Math. Logic,**38**(1), 61–77. arXiv: math/9801153 DOI: 10.1007/s001530050115 MR: 1667288 -
Abstract:

Let \omega 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 \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 §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. - Current version: 1998-01-12_10 (22p) published version (17p)

Bib entry

@article{Sh:626, author = {Jin, Renling and Shelah, Saharon}, title = {{Possible size of an ultrapower of $\omega$}}, journal = {Arch. Math. Logic}, fjournal = {Archive for Mathematical Logic}, volume = {38}, number = {1}, year = {1999}, pages = {61--77}, issn = {0933-5846}, mrnumber = {1667288}, mrclass = {03C20 (03C62 03E35 03E55 03H15)}, doi = {10.1007/s001530050115}, note = {\href{https://arxiv.org/abs/math/9801153}{arXiv: math/9801153}}, arxiv_number = {math/9801153} }