
doi: 10.1007/bf02808226
The author combines the techniques of Gitik's relative consistency proof of ``ZF \(+\) all uncountable cardinals are singular'' with his own consistency proof of ``ZF \(+\) uncountable cardinals are regular iff they are measurable'' to construct a model of ZF minus countable choice in which uncountable cardinals are measurable iff they are successors of singular cardinals. Moreover, in this model the successors of singular cardinals carry a normal measure. The consistency strength of this result is shown to be below the existence of an almost huge cardinal. The author also remarks that relative to some large cardinal assumption there is a model of ZF minus countable choice in which every second cardinal is measurable.
successors of singular cardinals, Large cardinals, axiom of choice, Axiom of choice and related propositions, consistency strength, measurable cardinal, ZF minus countable choice, Consistency and independence results, normal measure, almost huge cardinal
successors of singular cardinals, Large cardinals, axiom of choice, Axiom of choice and related propositions, consistency strength, measurable cardinal, ZF minus countable choice, Consistency and independence results, normal measure, almost huge cardinal
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