Recursively enumerable sets of polynomials over a finite field are Diophantine

DOI10.1007/s00222-007-0078-6zbMath1138.11055OpenAlexW1994166840MaRDI QIDQ2464706

Jeroen Demeyer

Publication date: 17 December 2007

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://biblio.ugent.be/publication/389620

zbMATH Keywords

Diophantine relationPolynomials over a finite fieldRecursively enumerable set

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Polynomials over finite fields (11T06) Recursively (computably) enumerable sets and degrees (03D25)

Related Items

NOTES ON THE DPRM PROPERTY FOR LISTABLE STRUCTURES ⋮ DIOPHANTINE SETS OF POLYNOMIALS OVER ALGEBRAIC EXTENSIONS OF THE RATIONALS ⋮ Bounded generation and commutator width of Chevalley groups: function case ⋮ Uniform existential interpretation of arithmetic in rings of functions of positive characteristic ⋮ Diophantine sets of polynomials over number fields

Cites Work

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• Recursively enumerable sets of polynomials over a finite field
• Diophantine classes of holomorphy rings of global fields
• Effective procedures in field theory
• Undecidability and Definability for the Theory of Global Fields
• Hilbert's Tenth Problem is Unsolvable
• Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of $\mathbb {Q}$
• Computable Algebra, General Theory and Theory of Computable Fields

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