A hierarchy of Ramsey-like cardinals
Volume 242 / 2018
Fundamenta Mathematicae 242 (2018), 49-74
MSC: 03E55, 03E35.
DOI: 10.4064/fm396-9-2017
Published online: 17 January 2018
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 (2011), and is based on certain infinite filter games, but 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.
