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y = 2x VS. y = 3x

Published online by Cambridge University Press:  12 March 2014

Alexei Stolboushkin  and
Damian Niwiński
Alexei Stolboushkin
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA, E-mail: aps@math.ucla.edu
Damian Niwiński
Affiliation:
Institute of Informatics, University of Warsaw, 02 097 Warsaw, Poland, E-mail: niwinski@mimuw.edu.pl
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Abstract

We show that no formula of first order logic using linear ordering and the logical relation y = 2x can define the property that the size of a finite model is divisible by 3. This answers a long-standing question which may be of relevance to certain open problems in circuit complexity.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 2 , June 1997 , pp. 661 - 672
Copyright
Copyright © Association for Symbolic Logic 1997

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