Implicit definability and infinitary languages

Abstract

In this paper we define the notions of invariant implicit definability (i.i.d.) and semi-invariant implicit definability (s.i.i.d.) on ε-models, A, of a certain weak set theory. These notions are intended to be the analogs of recursiveness and recursive enumerability, respectively. Following Barwise, with each A is associated an infinitary language whose formulas are elements of A.