Characterizing integers among rational numbers with a universal-existential formula
数论
2017-04-03 v1 逻辑
摘要
We prove that Z in definable in Q by a formula with 2 universal quantifiers followed by 7 existential quantifiers. It follows that there is no algorithm for deciding, given an algebraic family of Q-morphisms, whether there exists one that is surjective on rational points. We also give a formula, again with universal quantifiers followed by existential quantifiers, that in any number field defines the ring of integers.
引用
@article{arxiv.math/0703907,
title = {Characterizing integers among rational numbers with a universal-existential formula},
author = {Bjorn Poonen},
journal= {arXiv preprint arXiv:math/0703907},
year = {2017}
}
备注
6 pages