Possible size of an ultrapower of ω

Renling Jin*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let ω 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 ω, whose cardinality is (1) a singular strong limit cardinal, (2) a strongly inaccessible cardinal. This answers two questions in [1], modulo the assumption of supercompactness. In §2 we construct several λ-Archimedean ultrapowers of ω under some large cardinal assumptions. For example, we show that, assuming the consistency of a measurable cardinal, there may exist a λ-Archimedean ultrapower of ω for some uncountable cardinal λ. This answers a question in [8], modulo the assumption of measurability.

Original languageEnglish
Pages (from-to)61-77
Number of pages17
JournalArchive for Mathematical Logic
Volume38
Issue number1
DOIs
StatePublished - Jan 1999

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