Comparing inductive and circular definitions: Parameters, complexity and games
type: Item
instance of: scholarly article
title: Comparing inductive and circular definitions: Parameters, complexity and games
zbMATH Open document ID: 1098.03041
author: Kai-Uwe Kühnberger
author: Michael Möllerfeld
author: Benedikt Löwe
author: Philip D. Welch
published in: Studia Logica
publication date: 2006-03-17T00:00:00Z
review text: 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.
reviewed by: Albert A. Mullin
Mathematics Subject Classification ID: 03B99
Mathematics Subject Classification ID: 03D70
Mathematics Subject Classification ID: 91A80
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03C13
Mathematics Subject Classification ID: 03E60
zbMATH DE Number: 5013020
zbMATH Keywords: finite model theory
zbMATH Keywords: inductive definitions
zbMATH Keywords: revision theory of truth
zbMATH Keywords: circular definitions
MaRDI profile type: Publication
full work available at URL: s11225-005-2803-8
OpenAlex ID: W2148907430
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DOI: 10.1007/S11225-005-2803-8
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description: scientific article; zbMATH DE number 5013020