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22日(金)16:00〜
場所：zoom配信

講演者：Giovanni Solda (Ghent University)

題目　 A proof of Nash-Williams theorem in ATR0
概要　 In [1], Crispin Nash-Williams proved that if (Q, ≤_Q) is a well quasi-order (henceforth wqo), then so is the set of transfinite sequences over Q with finite range, ordered by embeddability. In this talk, we will show that this result is provable in the subsystem of second-order arithmetic ATR_0: together with previous results by Shore [2], this determines the reverse mathematical strength of Nash-Williams’ result. In order to do this, we will go via the notion of better quasi-order, which makes it possible to develop an equivalence between the iterated powerset of a qo Q and the iterated powerset over Q. This is joint work with Fedor Pakhomov.
[1] C. Nash-Williams, On well-quasi-ordering transfinite sequences, Mathematical Proceedings of the Cambridge Philosophical Society 61 (1965), no. 1, 33–39.
[2] R. A. Shore, On the strength of Fraïssé’s conjecture, Logical methods: In honor of Anil Nerode’s sixtieth birthday, 1993, pp. 782–813.