Characterizing Integers among Rational Numbers with a Universal-existential Formula
نویسنده
چکیده
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.
منابع مشابه
CHARACTERIZING INTEGERS AMONG RATIONAL NUMBERS WITH A UNIVERSAL-EXISTENTIAL FORMULA By BJORN POONEN
We prove that Z in definable in Q by a formula with two universal quantifiers followed by seven 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...
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