AbstractFor eachn> 0, two alternative axiomatizations of the theory of strings overnalphabetic characters are presented. One class of axiomatizations derives from Tarski's system of theWahrheitsbegriffand uses thencharacters and concatenation as primitives. The other class involves usingncharacter-prefixing operators as primitives and derives from Hermes'Semiotik. All underlying logics are second order. It is shown that, for eachn, 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.