Arithmetic on semigroups

Publisher： Cambridge University Press

E-ISSN： 1943-5886|74|1|265-278

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.74, Iss.1, 2009-03, pp. : 265-278

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Abstract

Relations between some theories of semigroups (also known as theories of strings or theories of concatenation) and arithmetic are surveyed. In particular Robinson's arithmetic Q is shown to be mutually interpretable with TC, a weak theory of concatenation introduced by Grzegorczyk. Furthermore, TC is shown to be interpretable in the theory F studied by Tarski and Szmielewa, thus confirming their claim that F is essentially undecidable.

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