An undecidability result for power series rings of positive characteristic. II

Author:

Pheidas Thanases

Abstract

We prove that the existential problem for a power series ring over an integral domain of positive characteristic with a predicate which represents the powers of the indeterminate is undecidable. We prove the same result for any ring which is contained in a power series ring and contains the corresponding ring of polynomials.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference13 articles.

1. Diophantine problems over local fields. III. Decidable fields;Ax, James;Ann. of Math. (2),1966

2. Further remarks on the elementary theory of formal power series rings;Becker, J.,1980

3. Definability in power series rings of nonzero characteristic;Cherlin, G. L.,1984

4. \bysame, Undecidability of rational function fields in nonzero characteristic, Logic Colloq., no. 82, North-Holland, Amsterdam.

5. Decision procedures for real and 𝑝-adic fields;Cohen, Paul J.;Comm. Pure Appl. Math.,1969

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