A Formalization of Set Theory without Variables

Abstract

The formalism $\mathcal L$of predicate logic The formalism $\mathcal L^+$, a definitional extension of $\mathcal L$ The formalism $\mathcal L^+$ without variables and the problem of its equipollence with $\mathcal L$ The relative equipollence of $\mathcal L$ and $\mathcal L^+$, and the formalization of set theory in $\mathcal L^\times$ Some improvements of the equipollence results Implications of the main results for semantic and axiomatic foundations of set theory Extension of results to arbitrary formalisms of predicate logic, and applications to the formalization of the arithmetics of natural and real numbers Applications to relation algebras and to varieties of algebras Bibliography Indices.