ウィキペディア英語版

出典:Wikipedia

Zero dagger

出典:『Wikipedia』 (2011/05/18 04:31 UTC 版)

英語による解説

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In set theory, 0 (zero dagger) is a particular subset of the natural numbers, first defined by Robert M. Solovay in unpublished work in the 1960s. (The superscriptshould be a dagger, but it appears as a plus sign on some browsers.) The definition is a bit awkward, because there might be no set of natural numbers satisfying the conditions. Specifically, if ZFC is consistent, then ZFC + "0 does not exist" is consistent. ZFC + "0 exists" is not known to be inconsistent (and most set theorists believe that it is consistent). In other words, it is believed to be independent (see large cardinal for a discussion). It is usually formulated as follows:

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