A new proof of the theorem on exponential diophantine representation of enumerable sets

DOI10.1007/BF01693980zbMath0449.03043OpenAlexW1968562989MaRDI QIDQ1147132

Yu. V. Matiyasevich

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1007/bf01693980

zbMATH Keywords

exponential diophantine representation of enumerable setsrecursively enumerable predicate

Mathematics Subject Classification ID

Applications of computability and recursion theory (03D80) Recursively (computably) enumerable sets and degrees (03D25) Diophantine equations (11D99) Connections of number theory and logic (11U99)

Related Items (7)

A direct method for simulating partial recursive functions by Diophantine equations ⋮ On the existential arithmetics with addition and bitwise minimum ⋮ How to Compute Antiderivatives ⋮ The complexity of antidifferentiation ⋮ Martin Davis and Hilbert’s Tenth Problem ⋮ A Story of Hilbert’s Tenth Problem ⋮ A normal form for arithmetical representation of \({\mathcal N}{\mathcal P}\)-sets

Cites Work

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• The decision problem for exponential diophantine equations
• Notes on Binomial Coefficients I-A Generalization of Lucas' Congruence†
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• A proof of negative answer to Hilbert's $10$th problem
• Reduction of an arbitrary diophantine equation to one in 13 unknowns
• An explicit diophantine definition of the exponential function
• Existential Definability in Arithmetic
• Arithmetical problems and recursively enumerable predicates

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