REVERSE MATHEMATICS, YOUNG DIAGRAMS, AND THE ASCENDING CHAIN CONDITION
Keyword(s):
AbstractLetSbe the group of finitely supported permutations of a countably infinite set. Let$K[S]$be the group algebra ofSover a fieldKof 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.
1987 ◽
Vol 52
(3)
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pp. 817-818
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1971 ◽
Vol 14
(3)
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pp. 443-444
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1974 ◽
Vol 26
(3)
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pp. 608-620
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1972 ◽
Vol 13
(4)
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pp. 433-446
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1968 ◽
Vol 9
(1)
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pp. 46-66
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1949 ◽
Vol 1
(2)
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pp. 125-152
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1970 ◽
Vol 22
(4)
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pp. 839-846
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2012 ◽
Vol 49
(3)
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pp. 366-389
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