Logical Hierarchy of Concepts

Abstract

Modern metalogical research falls, broadly, into two areas. The first, namely that concerned with models of axiomatic theories, has been described in the preceding chapter. The present chapter will be dedicated to the other area of metalogic, one aspect of which is indicated by the above heading. The other aspect might be formulated as: research on effectiveness of logical constructions. Both aspects are closely interconnected, since logical hierarchy of predicates consists mainly in singling out certain degrees of constructiveness or effectiveness of logical constructions. Moreover, analysis of effectiveness of logical constructions results in singling out those which are most effective. Such constructions are termed computable (general recursive or algorithmic). Hence, this branch of metalogic is mainly concerned with the investigations into such constructions. The present chapter will accordingly begin with such investigations.