Dan Nielsen : Mapping the Ramsey-like cardinals

Monday, December 18, 2017, 16.30
Seminar room 0.008, Mathematical Institute, University of Bonn

Speaker: Dan Nielsen (University of Bristol)

Title: Mapping the Ramsey-like cardinals


Ramsey-like cardinals were introduced in Gitman (2011) and Gitman & Welch (2011), broadly speaking being cardinals k that are critical points of elementary embeddings from a size k ZFC^- model. Recently, Holy & Schlicht (2017) have introduced a new large cardinal into the Ramsey-like family, called (strategic) alpha-Ramsey cardinals, whose distinctive feature is that they admit a game-theoretic characterisation. I will present some new results concerning how these Ramsey-like cardinals fit into the large cardinal hierarchy and how they interact with the core model K. This is joint work with Philip Welch.

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