Reverse mathematics, Young diagrams, and the ascending chain condition

Kostas Hatzikiriakou; Stephen G. Simpson

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arXiv · 1510.03106

Reverse mathematics, Young diagrams, and the ascending chain condition

Kostas Hatzikiriakou·Stephen G. Simpson

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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 RCA$_0$ (or even over RCA$_0^*$) to the statement that $ω^ω$ is well ordered. Our equivalence proof proceeds via the statement that the Young diagrams form a well partial ordering.

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BibTeX RIS

Kostas Hatzikiriakou, Stephen G. Simpson. 2015-10-11. Reverse mathematics, Young diagrams, and the ascending chain condition. https://arxiv.org/abs/1510.03106

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