Uniform existential interpretation of arithmetic in rings of functions of positive characteristic

• 成果类型: Article
• 署名作者: Pasten, Hector; Pheidas, Thanases; Vidaux, Xavier
• 署名单位: Queens University - Canada; University of Crete; Universidad de Concepcion
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0472-1
• 发表日期: 2014
• 页码: 453-484
• 关键词: hilberts 10th problem; algebraic function-fields; diophantine problems; polynomial-rings; undecidability; definability; sets

摘要

We show that first order integer arithmetic is uniformly positive-existentially interpretable in large classes of (subrings of) function fields of positive characteristic over some languages that contain the language of rings. One of the main intermediate results is a positive existential definition (in these classes), uniform among all characteristics p, of the binary relation or for some integer sa parts per thousand yen0. A natural consequence of our work is that there is no algorithm to decide whether or not a system of polynomial equations over has solutions in all but finitely many polynomial rings . Analogous consequences are deduced for the rational function fields , over languages with a predicate for the valuation ring at zero.