Recursion Theory/Descriptive Set Theory Seminar - Spring 2024
Time: Fridays 11:00-12:30
Location: 740 Evans Hall
Topic: Effective aspects of the Ramsey property, Mathias forcing, and Ramsey-type theorems.
Tentative Schedule:
- Jan 26. Yiping: Mathias's proof that analytic sets are Ramsey
- Feb 2. Katalin: Ellentuck's proof that analytic sets are Ramsey
- Feb 9. Forte. No analytic MAD families.
- Feb 16. Yvette: Mathias-Soare canonization
- Feb 23. Diego: Effective aspects of the Ramsey property
- Mar 1, 8. Alex T: BQO theory, Laver's proof of Fraïsse's conjecture, Pi^1_2 completeness of BQOs
- Mar 15, 22 Apr 5: Alex K and Clark: Borel graphs generated by single functions, \Sigma^1_2 completeness of finite colorability (3 lectures)
- David: The dual Ramsey theorem, its effective content, and canonization (2 lectures).
Guiding open questions:
- Does AD implies that all sets are Ramsey?
- Assume AD^+. Is is true that if G is a graph on the reals generated by a single function, then either G has a finite coloring, or there is a homomorphism from the shift graph G_s to G?
- Is every CBER hyperfinite on a Ramsey conull set?
- Is there a finite hyperarithmetic coloring of G_s restricted to the hyperarithmetic reals?
- What is the reverse mathematics strength of the dual ramsey theorem?
Other useful references: