Pointwise definable and Leibnizian extensions of models of arithmetic and set theory, Madison Logic Seminar, April 2023

Abstract. I shall present a new flexible method showing that every countable model of PA admits a pointwise definable-elementary end-extension. Also, any model of PA of size at most continuum admits an extension that is Leibnizian, meaning that any two distinct points are separated by some expressible property. Similar results hold in set theory, where one can also achieve V=L in the extension, or indeed any suitable theory holding in an inner model of the original model.

UW Madison Logic Seminar, Joel David Hamkins, April 4, 2023

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