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
Keywords Syntax  concatenation  foundations of logic  juxtaposition  Wahrheitsbegriff  truth-definition  categoricity  second-order logic  definitionally equivalent  character-prefixing
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Gualtiero Piccinini (2008). Computers. Pacific Philosophical Quarterly 89 (1):32–73.
John Corcoran (1980). Categoricity. History and Philosophy of Logic 1 (1):187-207.

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