DIOPHANTINE DEFINABILITY OVER HOLOMORPHY RINGS OF ALGEBRAIC FUNCTION FIELDS WITH INFINITE NUMBER OF PRIMES ALLOWED AS POLES-Reference-Cited by-同舟云学术

DIOPHANTINE DEFINABILITY OVER HOLOMORPHY RINGS OF ALGEBRAIC FUNCTION FIELDS WITH INFINITE NUMBER OF PRIMES ALLOWED AS POLES

Published:1998-12 Issue:08 Volume:09 Page:1041-1066
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

SHLAPENTOKH ALEXANDRA¹

Affiliation:

1. Department of Mathematics, East Carolina University, Greenville, NC 27858, USA

Abstract

Let K be an algebraic function field over a finite field of constants of characteristic greater than 2. Let W be a set of non-archimedean primes of K, let [Formula: see text]. Then for any finite set S of primes of K there exists an infinite set W of primes of K containing S, with the property that OK,S has a Diophantine definition over OK,W.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X98000440

Reference26 articles.

1. Hilbert's Tenth Problem is Unsolvable

2. The Diophantine problem for polynomial rings and fields of rational functions

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