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In set theory, 0† (zero dagger) is a particular subset of the natural numbers, first defined by Robert M. Solovay in unpublished work in the 1960s.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 superscript † should 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: :0† exists if and only if there exists a non-trivial elementary embedding ''j'' : ''L()'' → ''L()'' for the relativized Gödel constructible universe ''L()'', where ''U'' is an ultrafilter witnessing that some cardinal κ is measurable. If 0† exists, then a careful analysis of the embeddings of ''L()'' into itself reveals that there is a closed unbounded subset of κ, and a closed unbounded proper class of ordinals greater than κ, which together are ''indiscernible'' for the structure , and 0† is defined to be the set of Gödel numbers of the true formulas about the indiscernibles in ''L()''. Solovay showed that the existence of 0† follows from the existence of two measurable cardinals. It is traditionally considered a large cardinal axiom, although it is not a large cardinal, nor indeed a cardinal at all. == See also == *0#: a set of formulas (or subset of the integers) defined in a similar fashion, but simpler. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Zero dagger」の詳細全文を読む スポンサード リンク
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