Singular Cardinals Hypothesis
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High Quality Content by WIKIPEDIA articles! In set theory, the singular cardinals hypothesis (SCH) arose from the question of whether the least cardinal number for which the generalized continuum hypothesis (GCH) might fail could be a singular cardinal.Since SCH is a consequence of GCH which is known to be consistent with ZFC, SCH is consistent with ZFC. The negation of SCH has also been shown to be consistent with ZFC, if one assumes the existence of a sufficiently large cardinal number. In fact, by results of Moti Gitik, ZFC + the negation of SCH is equiconsistent with ZFC + the existence of a measurable cardinal of Mitchell order + + .…mehr

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High Quality Content by WIKIPEDIA articles! In set theory, the singular cardinals hypothesis (SCH) arose from the question of whether the least cardinal number for which the generalized continuum hypothesis (GCH) might fail could be a singular cardinal.Since SCH is a consequence of GCH which is known to be consistent with ZFC, SCH is consistent with ZFC. The negation of SCH has also been shown to be consistent with ZFC, if one assumes the existence of a sufficiently large cardinal number. In fact, by results of Moti Gitik, ZFC + the negation of SCH is equiconsistent with ZFC + the existence of a measurable cardinal of Mitchell order + + .