A+ CATEGORY SCIENTIFIC UNIT

Three-quantifier sentences

Volume 177 / 2003

Harvey M. Friedman 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]).

Authors

  • Harvey M. FriedmanDepartment of Mathematics
    Ohio State University
    Columbus, OH 43210, U.S.A.
    e-mail

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