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On revision operators

Published online by Cambridge University Press:  12 March 2014

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]

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2003

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