Reverse Mathematics (Summer 2026, TU Wien)

---

Time: Tuesdays, 10am (academic time, i.e., really 10:15).
Place: TU Wien, Freihaus. Zeichensaal 1 (8th floor, green area, behind the elevators).

• March 10th. Introduction. The language of Second-Order Arithmetic. Second-Order Arithmetic. Arithmetical Comprehension. Recursive Comprehension.
   
• March 24th. The arithmetical and analytical hierarchies. The "Big Five" systems: RCA0, WKL0, ACA0, ATR0, Pi11-CA0. Proof that RCA0 does not imply WKL0. The Jockush-Soare Low Basis Theorem and proof that WKL0 does not imply ACA0.
   
• March 31st. Lecture-free day.
   
• April 7th. Lecture-free day.
   
• April 14th. Miscellaneous Q&A. Coding  in RCA0: first-order part (tuples, functions, etc.). Finite Sigma01-CA in RCA0. Proof that ACA0 is equivalent to "every function on the natural numbers has a range."
   
• April 23rd. The integers, rationals, and reals in RCA0. Proof that the reals are not countable in RCA0. Proof that the Bolzano-Weierstrass theorem is equivalent to ACA0.
   
• April 28th. No lecture on the occasion of the Gödel birthday colloquium. Location: Boecksaal, TU Wien.
  https://sites.google.com/view/goedel26/event
   
• APRIL 30th (THURSDAY), 11:00–13:00 – MAKE-UP CLASS. Location: Seminar room 07 yellow.
   
• May 5th.
   
• May 12th. No lecture.
   
• May 19th.
   
• May 26th.
   
• June 2nd.
   
• June 9th.
   
• June 16th.
   
• June 23rd.  

[1] S. Simpson. Subsystems of second-order arithmetic (1999). Cambridge University Press.

[2] D. Dzhafarov and C. Mummert. Reverse Mathematics (2022). Springer. 

[3] J. Stillwell. Reverse Mathematics: Proofs from the Inside Out (2018). Princeton University Press.