DIOPHANTINE DEFINABILITY OVER HOLOMORPHY RINGS OF ALGEBRAIC FUNCTION FIELDS WITH INFINITE NUMBER OF PRIMES ALLOWED AS POLES

DOI10.1142/S0129167X98000440zbMath0920.11080OpenAlexW2002562642MaRDI QIDQ4235643

Alexandra Shlapentokh

Publication date: 1 June 1999

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129167x98000440

zbMATH Keywords

algebraic function fielddiophantine definitiondiophantine definability over holomorphic rings

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Decidability and field theory (12L05) Interpolation, preservation, definability (03C40)

Related Items (4)

Rational separability of the integral closure ⋮ Hilbert's tenth problem for rings of rational functions ⋮ 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

• Hilbert's tenth problem for fields of rational functions over finite fields
• Hilbert's Tenth Problem for rings of algebraic functions of characteristic 0
• Diophantine undecidability of \({\mathbb{C}{}}(t_ 1,t_ 2)\)
• A Diophantine definition of rational integers over some rings of algebraic numbers
• Diophantine unsolvability for function fields over certain infinite fields of characteristic \(p\)
• Diophantine undecidability in some rings of algebraic numbers of totally real infinite extensions of \(\mathbb{Q}\)
• 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
• The logic of pseudo-\(S\)-integers
• Diophantine unsolvability over \(p\)-adic function fields
• Diophantine undecidability over algebraic function fields over finite fields of constants
• Rational separability over a global field
• Extension of Hilbert's tenth problem to some algebraic number fields
• Diophantine relationships between algebraic number fields
• Hilbert's Tenth Problem for Rings of Algebraic Functions in One Variable Over Fields of Constants of Positive Characteristic
• Diophantine Sets over Some Rings of Algebraic Integers
• Questions of decidability and undecidability in Number Theory
• Diophantine undecidability for some holomorphy rings of algebraic functions of characteristic 0.
• Hilbert's Tenth Problem is Unsolvable
• Diophantine relations between rings of S-integers of fields of algebraic functions in one variable over constant fields of positive characteristic

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