Almost all Diophantine sets are undecidable

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2017 United States Publisher:Hikari, Ltd.Journal:International Mathematical Forum, volume 12, pages 803-806 (eissn: 1314-7536,

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Authors: Kreinovich, Vladik;

doi: 10.12988/imf.2017.7763

Almost all Diophantine sets are undecidable

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Abstract

The known 1970 solution to the 10th Hilbert problem says that no algorithm is possible that would decide whether a given Diophantine equation has a solution. In set terms, this means that not all Diophantine sets are decidable. In a posting to the Foundations of Mathematica mailing list, Timothy Y. Chow asked for possible formal justification for his impression that most Diophantine equations are not decidable. One such possible justification is presented in this paper.

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United States

Related Organizations

University of Texas at El Paso
United States

Keywords

Mathematics, 004, 510

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