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REVERSE MATHEMATICS, YOUNG DIAGRAMS, AND THE ASCENDING CHAIN CONDITION

Published online by Cambridge University Press:  19 June 2017

KOSTAS HATZIKIRIAKOU
Affiliation:
DEPARTMENT OF PRIMARY EDUCATION UNIVERSITY OF THESSALY ARGONAFTON & FILELLINON VOLOS38221, GREECE E-mail: kxatzkyr@uth.gr
STEPHEN G. SIMPSON
Affiliation:
DEPARTMENT OF MATHEMATICS 1326 STEVENSON CENTER VANDERBILT UNIVERSITY NASHVILLE, TN37240, USAURL: http://www.math.psu.edu/simpsonE-mail: sgslogic@gmail.com

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 $RC{A_0}$ (or even over $RCA_0^{\rm{*}}$) to the statement that ${\omega ^\omega }$ is well ordered. Our equivalence proof proceeds via the statement that the Young diagrams form a well partial ordering.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2017 

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