Coinductive formulas and a many-sorted interpolation theorem

Journal of Symbolic Logic 53 (3):937-960 (1988)
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 ω 1 ω-logic, which considers interpolation with respect to the language symbols, the quantifiers, the identity, and countably infinite conjunction and disjunction
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