for all infinite sets X X and Y Y. Proving this required most of the concepts and results from the second half of the course: well ordered sets, the Cantor–Bernstein theorem, the Hartogs theorem, Zorn ...

Nov 15, 2024 The penultimate week of this axiomatic set theory course, based on Lawvere’s Elementary Theory of the Category of Sets.

Hello [email protected]. So nice of you to stop by. I'm a member of the Theory Group here at UT. I've been at UT since September 1994. Before coming here, I was an Assistant Professor in the ...

We proved that all the usual things are equivalent to the axiom of choice: Zorn’s lemma, the well ordering principle, cardinal comparability (given two sets, one must inject into the other), and the ...

Earlier this month the Mathematics Institute at Uppsala University hosted a conference called Categorification in Algebra and Topology, clearly a theme close to our collective heart. As yet there are ...

This is the homepage for the UT Geometry and Quantum Field Theory Seminar. At the organizational meeting we will flesh out the details of our plans for the semester. Below are some suggestions to get ...

Previously: Part 5. Next: Part 7. A category theorist might imagine that a chapter with this title would be about constructing colimits, and they’d be half right.

every family of well ordered sets has a least member — informally, “the well ordered sets are well ordered”; ...

Aug 2, 2008 In this new version of our paper, we systematically explain how n-dimensional field theories give n-plectic manifolds. We also say how a B field affects the 2-plectic structure for a ...

Previously: Part 6. Next: Part 8. As the course continues, the axioms fade into the background. They rarely get mentioned these days. Much more often, the facts we’re leaning on are theorems that were ...

Apr 19, 2017 Conditional entropy, joint entropy and mutual information all have something important to say about the biological diversity of a metacommunity. Pre- and Postdictions of the NCG Standard ...