# Sh:626

• Jin, R., & Shelah, S. (1999). Possible size of an ultrapower of \omega. Arch. Math. Logic, 38(1), 61–77.
• 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.
• 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}
}