A structure of punctual dimension two

Abstract

This paper contributes to the general program which aims to eliminate an unbounded search from proofs and procedures in computable structure theory. A countable structure in a finite language is punctual if its domain is ω \omega and its operations and relations are primitive recursive. A function f f is punctual if both f f and f − 1 f^{-1} are primitive recursive. We prove that there exists a countable rigid algebraic structure which has exactly two punctual presentations, up to punctual isomorphism.