# String theory

*Journal of Symbolic Logic*39 (4):625-637 (1974)

**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.Staal, J. F.

Introduction to Mathematical Logic.Kleene, S. C.

Undecidable Theories.Davis, Martin

Introduction to mathematical logic.Church, Alonso

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Citations of this work BETA

Computing Mechanisms.Piccinini, Gualtiero

Sentence, Proposition, Judgment, Statement, and Fact: Speaking About the Written English Used in Logic.Corcoran, John

The Mind as Neural Software? Understanding Functionalism, Computationalism, and Computational Functionalism.Piccinini, Gualtiero

Computational Modeling Vs. Computational Explanation: Is Everything a Turing Machine, and Does It Matter to the Philosophy of Mind?Piccinini, Gualtiero

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