Defining Z in Q
成果类型：
Article
署名作者：
Koenigsmann, Jochen
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2016.183.1.2
发表日期：
2016
页码：
73-93
关键词：
摘要：
We show that Z is definable in Q by a universal first-order formula in the language of rings. We also present an for all there exists-formula for Z in Q with just one universal quantifier. We exhibit new diophantine subsets of Q like the complement of the image of the norm map under a quadratic extension, and we give an elementary proof for the fact that the set of nonsquares is diophantine.