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On revision operators

Published online by Cambridge University Press:  12 March 2014

P. D. Welch
P. D. Welch*
Affiliation:
Department of Mathematics, University of Bristol, Bristol BS8 1TW. England Graduate School of Science & Technology, Kobe University, Rokko-Dai. Nada-Ku, Kobe 657, Japan
*
Current address: Mathematisches Institut der Universität Bonn, Beringstr. 6, D-53115 Bonn, Germany, E-mail: [email protected]
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Abstract

We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta's theory of truth over arithmetic using fully varied revision sequences yields a complete Σ31 set of integers; (iii) the set of stably categorical sentences using their revision operator Ψ is similarly Σ31 and which is complete in GÖdel's universe of constructive sets L; (iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points.

Keywords

revision theorydefinability theoryadmissibility theorydescriptive set theory
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 2 , June 2003 , pp. 689 - 711
Copyright
Copyright © Association for Symbolic Logic 2003

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