$\prod_{1}^{0}$-POSITIVE INDUCTIVE DEFINABILITY ON ABSTRACT STRUCTURES

Abstract

Inductive definability by means of $\prod_{1}^{0}$-positive formulas is studied in the paper. An explicit characterization of the $\prod_{1}^{0}$-positive inductive sets on an arbitrary abstract structure with equality is presented. A relationship between these sets and the sets of all points of $\forall$-definedness of non-deterministic programs is established.