Geodesic
Three-quantifier sentences
Harvey M. Friedman1
1 Department of Mathematics Ohio State University Columbus, OH 43210, U.S.A.
Fundamenta Mathematicae, Tome 177 (2003) no. 3, pp. 213-240

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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]).
DOI : 10.4064/fm177-3-3
Keywords: complete proof quantifier sentences primitive notation set theory decided zfc weak fragment without power set axiom obtain information concerning witnesses quantifier formulas variable there quantifier sentence decided zfc see

Harvey M. Friedman 1

1 Department of Mathematics Ohio State University Columbus, OH 43210, U.S.A. 
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Harvey M. Friedman. Three-quantifier sentences. Fundamenta Mathematicae, Tome 177 (2003) no. 3, pp. 213-240. doi: 10.4064/fm177-3-3

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