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.

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 ...

You can now apply for the 2025 Summer Research Associate program at the Topos Institute! This is a really good opportunity. Details and instructions on how to apply are in the official announcement. 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 ...