# Proof or recursive unsolvability of Hilbert's tenth problem

@article{Jones1991ProofOR, title={Proof or recursive unsolvability of Hilbert's tenth problem}, author={James P. Jones and Yu. V. Matijasevi{\vc}}, journal={American Mathematical Monthly}, year={1991}, volume={98}, pages={689-709} }

(1991). Proof of Recursive Unsolvability of Hilbert's Tenth Problem. The American Mathematical Monthly: Vol. 98, No. 8, pp. 689-709.

## 51 Citations

Hilbert's Tenth Problem and Paradigms of Computation

- MathematicsCiE
- 2005

This is a survey of a century long history of interplay between Hilbert's tenth problem (about solvability of Diophantine equations) and different notions and ideas from the Computability Theory.

Martin Davis and Hilbert's Tenth Problem

- MathematicsMartin Davis on Computability, Computational Logic, and Mathematical Foundations
- 2016

The paper presents the history of the negative solution of Hilbert’s tenth problem , the role played in it by Martin Davis, consequent modifications of the original proof of DPRM-theorem, its…

A Direct Method for Simulating Partial Recursive Functions by Diophantine Equations

- MathematicsAnn. Pure Appl. Log.
- 1994

Computation Paradigms in Light of Hilbert's Tenth Problem

- Mathematics
- 2008

In the year 1900, the prominent German mathematician D. Hilbert delivered to the Second International Congress of Mathematicians (held in Paris) his famous lecture titled Mathematische Probleme [41].…

Elimination of quantifiers from arithmetical formulas defining recursively enumerable sets

- MathematicsMath. Comput. Simul.
- 2004

On the converse of Wolstenholme's Theorem

- Mathematics
- 1995

The problem of distinguishing prime numbers from composite numbers (. . .) is known to be one of the most important and useful in arithmetic. (. . .) The dignity of the science itself seems to…

On Certain Divisibility Property of Polynomials

- Mathematics
- 2010

We review the definition of D-rings introduced by H. Gunji & D. L. MacQuillan. We provide an alternative characterization for such rings that allows us to give an elementary proof of that a ring of…

Information-Theoretic Incompleteness

- Mathematics, Computer ScienceWorld Scientific Series in Computer Science
- 1992

We propose an improved definition of the complexity of a formal axiomatic system: this is now taken to be the minimum size of a self-delimiting program for enumerating the set of theorems of the…

On a Strange Recursion of Golomb

- MathematicsElectron. J. Comb.
- 1996

It is shown that, to the contrary, there are many increasing solutions for eachk, and it is indicated explicitly how to construct them.

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