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SELF-REFERENCE IN ARITHMETIC I

Published online by Cambridge University Press:  07 October 2014

VOLKER HALBACH  and
ALBERT VISSER
VOLKER HALBACH*
Affiliation:
Oxford University
ALBERT VISSER*
Affiliation:
Utrecht University
*
*NEW COLLEGE OXFORD, OX1 3BN, ENGLAND E-mail: volker.halbach@new.ox.ac.uk
†PHILOSOPHY, FACULTY OF HUMANITIES UTRECHT UNIVERSITY JANSKERHOF 13 3512 BL UTRECHT, THE NETHERLANDS E-mail: albert.visser@phil.uu.nl
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Abstract

A Gödel sentence is often described as a sentence saying about itself that it is not provable, and a Henkin sentence as a sentence stating its own provability. We discuss what it could mean for a sentence of arithmetic to ascribe to itself a property such as provability or unprovability. The starting point will be the answer Kreisel gave to Henkin’s problem. We describe how the properties of the supposedly self-referential sentences depend on the chosen coding, the formulae expressing the properties and the way a fixed points for the formulae are obtained. This paper is the first of two papers. In the present paper we focus on provability. In part II, we will consider other properties like Rosser provability and partial truth predicates.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 7 , Issue 4 , December 2014 , pp. 671 - 691
Copyright
Copyright © Association for Symbolic Logic 2014 

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