Journal of Symbolic Logic

String Theory

John Corcoran, William Frank, and Michael Maloney

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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.

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J. Symbolic Logic, Volume 39, Issue 4 (1974), 625-637.

First available in Project Euclid: 6 July 2007

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Corcoran, John; Frank, William; Maloney, Michael. String Theory. J. Symbolic Logic 39 (1974), no. 4, 625--637.

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