On Diophantine definability and decidability in some infinite totally real extensions of

Author:
Alexandra Shlapentokh

Journal:
Trans. Amer. Math. Soc. **356** (2004), 3189-3207

MSC (2000):
Primary 11U05, 11U09; Secondary 03C07

DOI:
https://doi.org/10.1090/S0002-9947-03-03343-9

Published electronically:
November 4, 2003

MathSciNet review:
2052946

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a number field, and a set of its non-Archimedean primes. Then let . Let be a finite set of prime numbers. Let be the field generated by all the -th roots of unity as and . Let be the largest totally real subfield of . Then for any , there exist a number field , and a set of non-Archimedean primes of such that has density greater than , and has a Diophantine definition over the integral closure of in .

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Additional Information

**Alexandra Shlapentokh**

Affiliation:
Department of Mathematics, East Carolina University, Greenville, North Carolina 27858

Email:
shlapentokha@mail.ecu.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03343-9

Keywords:
Hilbert's tenth problem,
Diophantine definability

Received by editor(s):
June 5, 2000

Received by editor(s) in revised form:
March 10, 2003

Published electronically:
November 4, 2003

Additional Notes:
The research for this paper has been partially supported by NSA grant MDA904-98-1-0510 and NSF grant DMS-9988620

Article copyright:
© Copyright 2003
American Mathematical Society