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Proving consistency of equational theories in bounded arithmetic

Published online by Cambridge University Press:  12 March 2014

Arnold Beckmann†*
Institut Für Mathematische Logik und Grundlagenforschung, Westfälische Wilhelms-Universität, Einsteinstr. 62, 48149 Münster, Germany, E-mail: Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, UK


We consider equational theories for functions denned via recursion involving equations between closed terms with natural rules based on recursive definitions of the function symbols. We show that consistency of such equational theories can be proved in the weak fragment of arithmetic S21. In particular this solves an open problem formulated by Takeuti (c.f. [5, p.5 problem 9.]).

Research Article
Copyright © Association for Symbolic Logic 2002

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