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The Mathematical Import of Zermelo's Well-Ordering Theorem

. The Bulletin of Symbolic Logic, 3 (3): 281--311 (1997)

Abstract

this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his...

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