Journal of Symbolic Logic

String Theory

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.

Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183739268

Mathematical Reviews number (MathSciNet)
MR398771

Zentralblatt MATH identifier
0298.02011

JSTOR