Defining integrality at prime sets of high density in number fields.

DOI10.1215/S0012-7094-00-10115-9zbMath1054.11064MaRDI QIDQ1974973

Alexandra Shlapentokh

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.dmj/1092749084

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Undecidability and degrees of sets of sentences (03D35) Totally real fields (11R80)

Related Items (15)

Rational separability of the integral closure ⋮ Defining the integers in large rings of a number field using one universal quantifier ⋮ ELLIPTIC CURVE POINTS AND DIOPHANTINE MODELS OF ℤ IN LARGE SUBRINGS OF NUMBER FIELDS ⋮ On Diophantine definability and decidability in some infinite totally real extensions of ℚ ⋮ Elliptic curves retaining their rank in finite extensions and Hilbert's Tenth Problem for rings of algebraic numbers ⋮ As easy as $\mathbb {Q}$: Hilbert’s Tenth Problem for subrings of the rationals and number fields ⋮ Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic ⋮ Extensions of Hilbert’s Tenth Problem: Definability and Decidability in Number Theory ⋮ Defining Integers ⋮ Diophantine definability and decidability in large subrings of totally real number fields and their totally complex extensions of degree 2 ⋮ Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of $\mathbb {Q}$ ⋮ Rings of algebraic numbers in infinite extensions of \(\mathbb Q\) and elliptic curves retaining their rank ⋮ Julia Robinson numbers ⋮ First-order definitions of rational functions and \({\mathcal S}\)-integers over holomorphy rings of algebraic functions of characteristic 0 ⋮ On Dipphantine definability and decidability in some rings of algebraic functions of characteristic 0

Cites Work

• Diophantine classes of holomorphy rings of global fields
• Diophantine definability over some rings of algebraic numbers with infinite number of primes allowed in the denominator
• Extension of Hilbert's tenth problem to some algebraic number fields
• Hilbert's Tenth Problem for a Class of Rings of Algebraic Integers
• Diophantine relationships between algebraic number fields
• Diophantine Sets Over Algebraic Integer Rings. II
• Hilbert's Tenth Problem for Quadratic Rings
• Diophantine Sets over Some Rings of Algebraic Integers
• Questions of decidability and undecidability in Number Theory
• Hilbert's Tenth Problem is Unsolvable
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Defining integrality at prime sets of high density in number fields.