The relative consistency of the class axioms of abstraction and extensionality and the axioms of NBG in a three-valued logic.
Ross T. Brady · Notre Dame Journal of Formal Logic · 1972
This paper is an extension of a previous one entitled "The Consistency of the Axioms of Abstraction and Extensionality in Three-Valued Logic'' [8].This proof differs from the one in [8] in that the structure M o (below) contains a model of NBG and the method of generating the sequence of structures, M o ^ M 1 ^ ... ^ M μ ^ ..., is more complicated.1.The formal system that we shall show to be relatively consistent to Z -F is the following: