Finite functions and the necessary use of large cardinals.
Three-quantifier sentences
We give a complete proof that all 3-quantifier sentences in the primitive notation of set theory (∈, =), are decided in ZFC, and in fact in a weak fragment of ZF without the power set axiom. We obtain information concerning witnesses of 2-quantifier formulas with one free variable. There is a 5-quantifier sentence that is not decided in ZFC (see [2]).
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