Rowbottom cardinals without the Axiom of Choice
نویسندگان
چکیده
We show that for all natural numbers n, the theory “ZF +DCאn + אω is a Rowbottom cardinal carrying a Rowbottom filter” has the same consistency strength as the theory “ZFC + There exists a measurable cardinal”. In addition, we show that the theory “ZF + אω1 is an ω2-Rowbottom cardinal carrying an ω2-Rowbottom filter and ω1 is regular” has the same consistency strength as the theory “ZFC + There exist ω1 measurable cardinals”. We also discuss some generalizations of these results.
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