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 22, 2024 The final chapter of this course on secretly-categorical set theory. Axiomatic Set Theory 9: The Axiom of Choice Nov 15, 2024 The penultimate week of this axiomatic set theory course, ...

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 ...

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

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 ...

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 ...

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

Nov 7, 2024 00:45 Here’s a way to argue that Gerard’s solution to my puzzle is correct. Thurston showed that any star of the ...

Nov 6, 2024 17:32 The photo shows a hexagonal antiprism. The diagram in the photo has two red vertices (or rather, a red vertex ...

Thurston gave a concrete procedure to construct triangulations of the 2-sphere where 5 or 6 triangles meet at each vertex. How can you get the icosahedron using this procedure? Gerard Westendorp has a ...