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]).
We prove that there exists a structure M whose monadic second order theory is decidable, and such that the first-order theory of every expansion of M by a constant is undecidable.
Una -tautologia è una tautologia del tipo avente un solo interpolante di Craig , a meno di equivalenza logica. Utilizzando misure di complessità relative al problema di trovare tale , mostriamo come si possano ottenere limiti non uniformi di complessità mediante limiti uniformi, e viceversa.