Algebra and Logic Seminar
Institute of Mathematics and Informatics, BAS Akad.G.Bonchev St, bl. 8, 1113, SofiaThe next meeting of the Algebra and Logic Seminar will be held on May 16, 2025 (Friday) at 1:00 pm (UTC+2) in Room 503 of IMI-BAS. A talk on: Grätzer-Schmidt Theorem in arithmetical transfinite recursion will be delivered by Soowhan Yoon (American University in Bulgaria). Abstract: We assess the reverse mathematical strength of the Grätzer-Schmidt theorem (GS) as a principle in second order arithmetic. The theorem GS was studied in an article by Katie Brodhead, Mushfeq Khan, Bjørn Kjos-Hanssen, William A. Lampe, Paul Kim Long V. Nguyen, and Richard A. Shore, where they establish the provability of GS in Π11 Comprehension (Π11-CA0) and its restrictive variant GSD in arithmetical comprehension (ACA0). It will be shown that the arithmetical transfinite recursion (ATR0) is sufficient to prove GS. [...]