Comparing inductive and circular definitions: Parameters, complexity and games
Recall that in the revision theory of truth we have a base language which, for simplicity, is usually taken as first-order (axiomatic) arithmetic. Then we search to define the extension of an additional predicate by semantic rules. In this comprehensive paper, the authors investigate the underlying logical methodologies of inductive definitions and circular definitions (in a vague sense, the next step after inductive definitions). Using game-theoretic representations (say, in the sense of Y. N. Moschovakis's game quantifier) they discuss ways in which inductive and circular definitions form different levels of a hierarchy. Several theorems are proved in great detail. The reviewer looks forward to the treatment of analogical definitions as the next step after circular definitions.
scientific article; zbMATH DE number 5013020
scientific article