Three-quantifier sentences
Volume 177 / 2003
Fundamenta Mathematicae 177 (2003), 213-240
MSC: Primary 03E30; Secondary 03B25.
DOI: 10.4064/fm177-3-3
Abstract
We give a complete proof that all $3$-quantifier sentences in the primitive notation of set theory ($\in ,=$), 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]).
