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A hierarchy of Ramsey-like cardinals

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)49-74
Number of pages26
JournalFundamenta Mathematicae
Early online date17 Jan 2018
DateAccepted/In press - 27 Oct 2017
DateE-pub ahead of print - 17 Jan 2018
DatePublished (current) - Jan 2018


We introduce a hierarchy of large cardinals between weakly compact and measurable cardinals, that is closely related to the Ramsey-like cardinals introduced by Victoria Gitman, and is based on certain infinite filter games, however also has a range of equivalent characterizations in terms of elementary embeddings. The aim of this paper is to locate the Ramsey-like cardinals studied by Gitman, and other well-known large cardinal notions, in this hierarchy.

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