DIOPHANTINE SETS OF POLYNOMIALS OVER ALGEBRAIC EXTENSIONS OF THE RATIONALS

DOI10.1017/jsl.2013.9zbMath1355.03034OpenAlexW2103760253MaRDI QIDQ2933672

Claudia Degroote, Jeroen Demeyer

Publication date: 5 December 2014

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://biblio.ugent.be/publication/4128161

zbMATH Keywords

recursively enumerable setsDiophantine setsHilbert's tenth problem

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Decidability of theories and sets of sentences (03B25) Applications of computability and recursion theory (03D80) Recursively (computably) enumerable sets and degrees (03D25)

Related Items (1)

NOTES ON THE DPRM PROPERTY FOR LISTABLE STRUCTURES

Cites Work

• Diophantine unsolvability over \(p\)-adic function fields
• Hilbert's tenth problem for rational function fields over \(p\)-adic fields
• Recursively enumerable sets of polynomials over a finite field are Diophantine
• Effective procedures in field theory
• Diophantine sets of polynomials over number fields
• Hilbert's Tenth Problem is Unsolvable
• A decision method for $p$-adic integral zeros of diophantine equations

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