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.
• Version 1998-01-12_10 (22p) published version (17p)

@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}
}