How to find pointwise definable and Leibnizian extensions of models of arithmetic and set theory, Oxford Logic Seminar, May 2023

This will be a talk (in person) for the Logic Seminar of the Mathematics Institute of the Univerisity of Oxford, May 18, 2023 5pm, Wiles Building L3.

By Alain Goriely - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=29752669

Abstract:  I shall present a new flexible method showing that every countable model of PA admits a pointwise definable end-extension, one in which every point is definable without parameters. 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.

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

Pointwise definable and Leibnizian extensions of models of arithmetic and set theory, MOPA seminar CUNY, November 2022

 This will be an online talk for the MOPA Seminar at CUNY on 22 November 2022 1pm. Contact organizers for Zoom access.

Abstract. 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.