Is there a least transitive model of Kelley-Morse set theory?

by kamerynwilliams

This was a talk at the CUNY set theory seminar. Like many questions which appear as titles of talks or articles or etc., the answer is no.

It’s well-known that there is a least transitive model of ZFC. Namely, L_\alpha, where \alpha is the least ordinal which is the \mathrm{Ord} of a model of set theory is contained in every transitive model of ZFC. With a little bit of effort, one can extend this to see that there is a least transitive model of GBC; its first-order part is L_\alpha and its second-order part is the definable classes. Can we extend this result further to get that there is a least transitive model of KM? The purpose of this talk is to answer this question in the negative.

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