Abstraction and definability in semantically closed structures (Q1084389)

Tarski's noted theorem on undefinability of truth depends on the underlying logic. \textit{S. Kripke} [J. Philos. 72, No.19, 690-719 (1975)] added the third logical value ''undefined'', and defined truth in the resulting system. The paper under review concerns the definability of sets in the set theory based on Kripke's system. A set X is definable if there is a formula satisfied exactly by the elements of X. It is proved that there is a formula such that the sets defined by it and by its negation do not exhaust the universe.