November 22
Joel David Hamkins, University of Notre Dame
Pointwise definable and Leibnizian extensions of models of arithmetic and set theory

I shall introduce a flexible new method showing that every countable model of PA admits a pointwise definable end-extension, one in which every individual is definable without parameters. And similarly for models of set theory, in which one may also achieve the Barwise extension result—every countable model of ZF admits a pointwise definable end-extension to a model of ZFC+V=L, or indeed any theory arising in a suitable inner model. A generalization of the method shows that every model of arithmetic of size at most continuum admits a Leibnizian extension, and similarly in set theory.