Set theory with abundant urelements, STUK 10, Oxford, June 2023

This will be a talk for the Set Theory in the UK, STUK 10, held in Oxford 14 June 2023, organized by my students Clara List, Emma Palmer, and Wojciech Wołoszyn.

Abstract. I shall speak on the surprising strength of the second-order reflection principle in the context of set theory with abundant urelements. The theory GBcU with the abundant urelement axiom and second-order reflection is bi-interpretable with a strengthening of KM with a supercompact cardinal. This is joint work with Bokai Yao.

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