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：11月1日(金)14:30〜
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 (小山高専)

題目　 On some restricted variants of the leftmost path principle
概要　 In the studies of reverse mathematics and problem reductions, principles stating the existence of a path through a given tree play a central role.
For example, WKL, KL, C_{ω^ω} and LPP are widely studied in those contexts.
Here, WKL is the assertion that any infinite binary tree has a path, KL is the assertion that any finitely branching infinite tree has a path, C_{ω^ω} is the principle to find a path from an ill-founded tree, and LPP is the assertion that any ill-founded tree has a leftmost path.
Recently, Towsner[Tow] introduced a new principle called the relative leftmost path principle stating the existence of a pseudo leftmost path.
It is known that the proof-theoretic strength of relative LPP is strictly between ATR_0 and Pi^1_1-CA_0, and relative LPP is useful to study the complexity of some theorems which are stronger than ATR_0[FDSTY].
In this talk, I will present my contribution[SuY, Suz] to the studies of relative LPP, and consider LPP and relative LPP restricted to WKL or KL.
A part of this talk is joint work with Keita Yokoyama.
[Tow] Henry Towsner. Partial impredicativity in reverse mathematics. J. Symb. Log., 78(2):459–488, 2013
[FDSTY] David Fern´andez-Duque, Paul Shafer, Henry Towsner, and Keita Yokoyama. Metric fixed point theory and partial impredicativity. Philosophical Transactions of the Royal Society A, 381(2248):20220012, 2023.
[SuY] Yudai Suzuki and Keita Yokoyama. Ann. Pure Appl. Logic 175, No. 10, Article ID 103488, 31 p. (2024; Zbl 07894021)
[Suz] Yudai Suzuki Relative leftmost path principles and omega-model reflections of transfinite inductions’, Preprint, arXiv:2407.13504 [math.LO] (2024)