Completeness and Decidability of the Deducibility Problem for Some Classes of Formulas of Set Theory

Abstract

Some extension of results on the decidability of classes of formulas in set theory is proved. In particular some class of restricted quantified formulas is proved to be decidable also in the case in which the underlying axiomatic set theory does not contain the axiom of foundation. For all the classes considered is also studied whether or not they result to be not only decidable, but also complete and a simple decidable but not complete class of formulas is presented.