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Some new upper bounds in consistency strength for certain choiceless large cardinal patterns. (English) Zbl 0755.03028
Assuming the existence of an almost huge cardinal, Gitik and the author have proved the existence of various models of \(\text{ZF}+\neg\text{AC}_ \omega\) in which large classes of cardinals are singular (e.g. a model of ZF in which all uncountable nonmeasurable cardinals are singular). Using the method of extenders, the author improves these results by weakening the assumption in consistency strength.

MSC:
03E60 Determinacy principles
03E55 Large cardinals
03E35 Consistency and independence results
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