A direct method for simulating partial recursive functions by Diophantine equations

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Abstract

A new proof is given of the celebrated theorem of M. Davis, H. Putnam and J. Robinson concerning exponential Diophantine representation of recursively enumerable predicates. The proof goes by induction on the defining scheme of a partial recursive function.

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The paper was written during author's stay at Laboratoire de Recherche en Informatique de Université Paris-XI in the framework of a program of collaboration between the Steklov Institute of Mathematics and the Universities Paris-VI, Paris-VII and Paris-XI, sponsored by CNRS.