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Undecidability in diagonalizable algebras

Published online by Cambridge University Press:  12 March 2014

V. Yu. Shavrukov
V. Yu. Shavrukov*
Affiliation:
Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
*
Department of Philosophy, Utrecht University, Heidelberglaan 8, 3584 CS Utrecht, The Netherlands, E-mail: volodya@phil.ruu.nl
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Abstract

If a formal theory T is able to reason about its own syntax, then the diagonalizable algebra of T is defined as its Lindenbaum sentence algebra endowed with a unary operator □ which sends a sentence φ to the sentence □φ asserting the provability of φ in T. We prove that the first order theories of diagonalizable algebras of a wide class of theories are undecidable and establish some related results.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 1 , March 1997 , pp. 79 - 116
Copyright
Copyright © Association for Symbolic Logic 1997

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