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• W3100596403 abstract "We study a transfinite iteration of the ordinal Hessenberg natural sum obtained by taking suprema at limit stages. We show that such an iterated natural sum differs from the more usual transfinite ordinal sum only for a finite number of iteration steps. The iterated natural sum of a sequence of ordinals can be obtained as a mixed sum (in an order-theoretical sense) of the ordinals in the sequence; in fact, it is the largest mixed sum which satisfies a finiteness condition. We introduce other infinite natural sums which are invariant under permutations and show that all the sums under consideration coincide in the countable case." @default.
• W3100596403 created "2020-11-23" @default.
• W3100596403 creator A5074414706 @default.
• W3100596403 date "2018-12-01" @default.
• W3100596403 modified "2023-09-26" @default.
• W3100596403 title "Some transfinite natural sums" @default.
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• W3100596403 doi "https://doi.org/10.1002/malq.201600092" @default.
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