Infinitely Many Precomplete with Respect to Parametric Expressibility Classes of Formulas in a Provability Logic of Propositions

Abstract

In the present paper we consider a non-tabular extension L of the well-known propositional provability logic GL together with the notion of parametric expressibility of formulas in a logic proposed by A. V. Kuznetsov. We prove that there are infinitely many precomplete with respect to parametric expressibility classes of formulas in the above mentioned logic L.

Keywords

• parametric expressibility of formulas
• modal logic
• diagonalizable algebra
• precomplete classes of formulas with respect to parametric expressibility
• extensions of logics