皆様，

東北大学の竹田です． 以下の通りセミナーを開催いたしますのでご案内いたします．

https://sites.google.com/view/sendai-logic/

日時：5月24日(金)15:00〜 場所：東北大学理学研究科合同A棟801号室 (zoom配信あり)

講演者：鈴木悠大 (国立沖縄高専)

題目　 On the Pi^1_2, Sigma^1_2 and Boole(Pi^1_2) sentences provable from Pi^1_1-CA_0 概要　In [1], we introduced some characterizations of the set of Pi^1_2 sentences provable from Pi^1_1-CA_0 and a hierarchy dividing it. For a detailed study of the properties of this hierarchy, it was important to focus on the statements of the form [every coded beta-model satisfies sigma] for some specific sentences sigma. In this talk, we summarize a part of [1]. Then we give a characterization of the set of Sigma^1_2 or Boole(Pi^1_2) sentences provable from Pi^1_1-CA_0 by statements of the form [every coded beta-model satisfies sigma]. Here, Boole(Pi^1_2) is the class of formulas generated by disjunction, conjunction and negation starting from Pi^1_2. This is joint work with J. Aguilera and K. Yokoyama. [1] Suzuki, Y., & Yokoyama, K. (2024). On the $\Pi^ 1_2 $ consequences of $\Pi^ 1_1 $-$\mathsf {CA} _0$. arXiv preprint arXiv:2402.07136.

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竹田 侑人 [email protected]