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The dimension of the negation of transitive closure

Published online by Cambridge University Press:  12 March 2014

Gregory L. McColm
Gregory L. McColm*
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 33620, E-mail: mccolm@math.usf.edu
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Abstract

We prove that any positive elementary (least fixed point) induction expressing the negation of transitive closure on finite nondirected graphs requires at least two recursion variables.

Keywords

Finite model theorycomputational expressibilitypebble gamestransitive closureconnectivityfixedpoint logicnumber of variables
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 2 , June 1995 , pp. 392 - 414
Copyright
Copyright © Association for Symbolic Logic 1995

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