Operational Variables and Meta-theorems

Abstract

This paper deals with the notion of an operational variable in metalogical contexts. After a clarification of the notion itself through an example concerning identity of reference, a few meta-theorems regarding the property of theoremicity are presented. These meta-theorems articulate, with a high degree of generality, the concepts of a set of formulae, deducibility and operation over sets. Operational variables are shown to be useful for stating some interesting results in classical logic. Such results guarantee the intelligibility of the notion of an operational variable, as no extra-logical concepts are employed in the proofs, but only well-known notions and rules.