• Publications
  • Influence
The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions
In this work, the deployment of cache coherence is disproved and Leat, the new system for reliable models, is the solution to all of these issues.
On the number of solutions of Diophantine equations
For any nontrivial set of cardinal numbers _bt, it is shown that there is no algorithm for testing whether or not the number of positive integer solutions of a given polynomial Diophantine equation
The Incompleteness Theorem
  • Martin Davis
  • Philosophy
    The Incompleteness Phenomenon
  • 8 October 2018
414 NOTICES OF THE AMS VOLUME 53, NUMBER 4 I n September 1930 in Königsberg, on the third day of a symposium devoted to the foundations of mathematics, the young Kurt Gödel launched his bombshell
Abstract : The report describes an application of recursive function theory to Hilbert's tenth problem. It is proved that if a particular exhibited diophantine equation has no nontrivial solutions,
Extensions and Corollaries of Recent Work on Hilbert's Tenth Problem
Abstract : The theorem that every recursively enumerable set is expon ntial Diophantine is improve ; a sharp form is given of Kleene's (Introduction to Metamathematics, D. Van Nostrand Company, Inc.,