∏10-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 $\mathrm{\forall }$-definedness of non-deterministic programs is established.