General Logic-Systems and Consequence Operators

Abstract

In this paper, general logic-systems are investigated. It is shown that there are infinitely many finite consequence operators defined on a fixed language L that cannot be generated from a finite logic-system. It is shown that a set map is a finite consequence operator iff it is defined by a general logic-system.

Only 5 pages. In this version, the definition of RI* is replaced by the one that appears in the expanded published version of this paper