String theory

Journal of Symbolic Logic 39 (4):625-637 (1974)
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Abstract
For each positive n , 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 definitionally equivalent [or 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 definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories
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References found in this work BETA
Syntactic Structures.Chomsky, Noam; Luce, R. Duncan; Bush, Robert R. & Galanter, Eugene
Mathematical Logic.White, Morton G. & Quine, Willard Van Orman

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Citations of this work BETA
Computing Mechanisms.Piccinini, Gualtiero
The Good, the Bad and the Ugly.Ebert, Philip & Shapiro, Stewart

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2009-01-28

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