Violating the Singular Cardinals Hypothesis Without Large Cardinals

نویسنده

  • Peter Koepke
چکیده

Easton proved that the behavior of the exponential function 2 at regular cardinals κ is independent of the axioms of set theory except for some simple classical laws. The Singular Cardinals Hypothesis SCH implies that the Generalized Continuum Hypothesis GCH 2 = κ holds at a singular cardinal κ if GCH holds below κ. Gitik and Mitchell have determined the consistency strength of the negation of the Singular Cardinals Hypothesis in Zermelo Fraenkel set theory with the axiom of choice AC in terms of large cardinals.

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تاریخ انتشار 2010