# Talk: Mapping the Ramsey-like cardinals

On December 18, I will be giving an invited talk at the Bonn Logic Seminar.

Abstract. Ramsey-like cardinals were introduced in Gitman (2011) and Gitman & Welch (2011), broadly speaking being cardinals $\kappa$ that are critical points of elementary embeddings from a size $\kappa$ $\textsf{ZFC}^-$-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.

• Gitman, Victoria: “Ramsey-like cardinals”, JSL 76 (2011), no. 2, 519-540
• Gitman, Victoria and Welch, Philip D.: “Ramsey-like cardinals II”, JSL 76 (2011), no. 2, 541-560
• Holy, Peter and Schlicht, Philipp: “A hierarchy of Ramsey-like cardinals”, preprint (2017), arXiv:1710.10043.