http://worldcat.org/entity/work/id/137162391

Decision procedures for real and p-adic fields

A decision procedure is given for the real number field which reproves a result of Tarski, and for p-adic fields a procedure is given to reduce problems about the field to statements concerning the residue class rings. This gives a purely effective proof of the recent results of Ax and Kochen. The methods used point up the similarity of the two cases. Thus whereas Sturm's theorem can be used in the real case, our proof yields an inductive procedure for finding roots in the p-adic case. Finally, the application to Artin's conjecture is discussed and it is shown that the exceptional primes are primitive recursive functions of the degree. (Author).

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