• Venue: Complex A 801 (and online via zoom)

Time: 14:30-16:00

Abstract: 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)