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String theory

Published online by Cambridge University Press:  12 March 2014

John Corcoran
Affiliation:
State University of New York at Buffalo, Amherst, New York 14226
William Frank
Affiliation:
State University of New York at Buffalo, Amherst, New York 14226
Michael Maloney
Affiliation:
State University of New York at Buffalo, Amherst, New York 14226

Abstract

For each n > 0, two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are synonymous in the sense of deBouvere. It is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are synonymous with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1974

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References

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