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Hereditary undecidability of some theories of finite structures

Published online by Cambridge University Press:  12 March 2014

Ross Willard
Ross Willard*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, E-mail: rdwillar@flynn.uwaterloo.ca
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Abstract

Using a result of Gurevich and Lewis on the word problem for finite semigroups, we give short proofs that the following theories are hereditarily undecidable: (1) finite graphs of vertex-degree at most 3; (2) finite nonvoid sets with two distinguished permutations; (3) finite-dimensional vector spaces over a finite field with two distinguished endomorphisms.

Keywords

Undecidable theoryinterpretablefinite graphsfinite modulesword problem
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 4 , December 1994 , pp. 1254 - 1262
Copyright
Copyright © Association for Symbolic Logic 1994

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