Diophantine definability and decidability in large subrings of totally real number fields and their totally complex extensions of degree 2

DOI10.1006/jnth.2001.2759zbMath1082.11079OpenAlexW2080689220MaRDI QIDQ701108

Alexandra Shlapentokh

Publication date: 16 October 2002

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/1d8d207e99688dcd18b868ece5c697963f68dd95

Mathematics Subject Classification ID

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

Related Items (12)

Diophantine definability and decidability in extensions of degree 2 of totally real fields ⋮ Defining the integers in large rings of a number field using one universal quantifier ⋮ 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 ⋮ 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 ⋮ Diophantine undecidability of holomorphy rings of function fields of characteristic 0 ⋮ First-order definitions of rational functions and \({\mathcal S}\)-integers over holomorphy 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
• Defining integrality at prime sets of high density in number fields.
• Extension of Hilbert's tenth problem to some algebraic number fields
• Hilbert's Tenth Problem for a Class of Rings of Algebraic Integers
• 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
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