Coinductive Formulas and a Many-Sorted Interpolation Theorem

Abstract

We use connections between conjunctive game formulas and the theory of inductive definitions to define the notions of a coinductive formula and its approximations. Corresponding to the theory of conjunctive game formulas we develop a theory of coinductive formulas, including a covering theorem and a normal form theorem for many sorted languages. Applying both theorems and the results on "model interpolation" obtained in this paper, we prove a many-sorted interpolation theorem for $\omega_1\omega$-logic, which considers interpolation with respect to the language symbols, the quantifiers, the identity, and countably infinite conjunction and disjunction.