Seminar Details
Finite Axioms of Choice
- Start Date: October 27, 2021
- Event Start Time: 3:00 PM
- Event End Time: 4:00 PM
- Seminar Series: Graduate Combinatorics Seminar
- Presenter(s): Brian Pinsky - Rutgers University
- Event Location: Mathematics Graduate Student Lounge -- 7th Floor | Rutgers University | Hill Center | Mathematics Department
- Event Additional Info: <p><strong>This seminar is being held in person in The Hill Center,<br /> Mathematics Graduate Student Lounge - 7th Floor<br /> and online via a simultaneous broadcast on Zoom. </strong><br /> Zoom Link: <a href="https://rutgers.zoom.us/j/95142025758?pwd=VXJRU3VPbUhNY2RIMXBiZTZLTHhTdz09">https://rutgers.zoom.us/j/95142025758</a></p> <p>Password: 557818</p> <p>For further information see: <a href="https://sites.math.rutgers.edu/~ctk47/GCS.html">https://sites.math.rutgers.edu/~ctk47/GCS.html</a></p>
- Presentation Type: Stand Alone Presentation
- Abstract:
The axiom of choice says "every set of non-empty sets has a choice function". This has some well known, slightly problematic consequences. However, abandoning AC can result in much much worse consequences (e.g. the reals are a countable union of countable sets). This has led mathematicians think of lots of weaker axioms over the year.
In this talk, I'll give an overview of a bunch of several of these axioms. Some are stronger than others, but which ones are how strong can be hard to tell. The axioms "every set of n-element sets have a choice function" turn out particularly interesting; studying the implications will take us through some vary fancy combinatorics, and a presumably open question that's been bothering me for like years now.