希尔伯特的第十题

100 Years of Math Milestones Pub Date : 2019-06-12 DOI:10.1090/mbk/121/58

Andrew J. Misner

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引用次数: 0

摘要

在下面的文章中，我将简要介绍丢番图集理论和可计算性理论。然后，我将介绍Matiyasevich-Robinson-Davis-Putnam (MRDP)定理，只要对数学基础有粗略的了解，就可以立即理解它，并给出一些证明的细节。最后，我将介绍一些在丢芬图可计算性领域的进一步工作，以及著名的MRDP定理的各种应用或推论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hilbert’s tenth problem

In the following paper, I will give a brief introduction to the theory of Diophantine sets as well as the theory of computability. I will then present the Matiyasevich-Robinson-Davis-Putnam (MRDP) theorem, which is immediately comprehensible given just a cursory understanding of the mathematical basics, and give some details of its proof. Finally, I will present some further work in the area of Diophantine computability and various applications or corollaries of the celebrated MRDP theorem.

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