Reverse mathematics, young diagrams, and the ascending chain condition

Abstract

Let S be the group of finitely supported permutations of a countably infinite set. Let K[S] be the group algebra of S over a field K of characteristic 0. According to a theorem of Formanek and Lawrence, K[S] satisfies the ascending chain condition for two-sided ideals. We study the reverse mathematics of this theorem, proving its equivalence over RCA0 (or even over RCA0 ∗) to the statement that ωω is well ordered. Our equivalence proof proceeds via the statement that the Young diagrams form a well partial ordering. © 2017 The Association for Symbolic Logic.