用普适存在公式刻画有理数中的整数
Characterizing integers among rational numbers with a universal-existential formula
摘要：
我们证明了Z在Q中可由一个公式定义，该公式有2个全称量词和7个存在量词。由此可见，对于给定的一个代数族Q-态射，没有算法可以判定是否存在一个在有理点上满射的代数族。我们还给出了一个公式，再次与全称量词后跟存在量词，在任何数域中定义的整数环。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
