A hierarchy of Ramsey-like cardinals

Peter Holy; Philipp Schlicht

doi:10.4064/fm396-9-2017

A hierarchy of Ramsey-like cardinals

Peter Holy, Philipp Schlicht

School of Mathematics

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Abstract

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.

Original language	English
Pages (from-to)	49-74
Number of pages	26
Journal	Fundamenta Mathematicae
Volume	242
Early online date	17 Jan 2018
DOIs	https://doi.org/10.4064/fm396-9-2017
Publication status	Published - Jan 2018

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https://arxiv.org/abs/1710.10043

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AB - 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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DO - 10.4064/fm396-9-2017

M3 - Article (Academic Journal)

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JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

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A hierarchy of Ramsey-like cardinals

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