Extensions and Corollaries of Recent Work on Hilbert's Tenth Problem

Abstract : The theorem that every recursively enumerable set is expon ntial Diophantine is improve ; a sharp form is given of Kleene's (Introduction to Metamathematics, D. Van Nostrand Company, Inc., 1952) normal form theorem, a problem of Quine (Synthese, VII; 441-46, 1948-9) is proved recursively unsolvable. (Author)