Title: A recursive pairing function for the algebraic reals
Archive date: 2 September 1994
Abstract: Friedman and Mansfield \cite{friman:1990} discuss the existence of recursive pairing functions over various fields. They show that a field of infinite transcendence degree does not have a pairing function and that if we allow $<$ as an atomic relation, an Archimedean ordered field of finite transcendence degree does have a pairing function. They explicitly list the case of the algebraic reals without $<$ as an open problem.
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