На 16 май 2025 г. (петък) от 13:00 часа в зала 503 на ИМИ
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Доклад на тема:

Grätzer-Schmidt Theorem in arithmetical transfinite recursion

ще изнесе

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. Additionally, other variants of GS will be explored as well. Some will be proved in ACA₀, while others will be shown equivalent to ATR₀ over ACA₀. Then, we will discuss these results in the context of “Almost Theorems of Hyperarithmetic Analysis” (ATHA) by Shore in 2023.

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http://www.math.bas.bg/algebra/seminarAiL/
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