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Arithmetic on semigroups

Published online by Cambridge University Press:  12 March 2014

Mihai Ganea
Mihai Ganea*
Affiliation:
Department of Philosophy, Boston University, Boston, Ma 02215, USA, E-mail: mganea@bu.edu
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Abstract

Relations between some theories of semigroups (also known as theories of strings or theories of concatenation) and arithmetic are surveyed. In particular Robinson's arithmetic Q is shown to be mutually interpretable with TC, a weak theory of concatenation introduced by Grzegorczyk. Furthermore, TC is shown to be interpretable in the theory F studied by Tarski and Szmielewa, thus confirming their claim that F is essentially undecidable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 1 , March 2009 , pp. 265 - 278
Copyright
Copyright © Association for Symbolic Logic 2009

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