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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 377, Pages 50–54
(Mi znsl3813)
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This article is cited in 2 scientific papers (total in 2 papers)
Representation theorems for r.e. sets and a conjecture related to Poonen's larges subring of $\mathbb Q$
M. Davisab a Courant Inst., NYU
b Visting Scholar, Univ. Calif. Berkeley
Abstract:
It is remarked that unsolvability results can often be extended to yield novel “representation” theorems for the set of all recursively enumerable sets. In particular it is shown that analysis of the proof of the unsolvability of Hilbert's 10th Problem over Poonen's large subring of $\mathbb Q$ can provide such a theorem. Moreover, applying that theorem to the case of a simple set leads to a conjecture whose truth would imply the unsolvability of Hilbert's 10th Problem over $\mathbb Q$. Bibl. 7 titles.
Key words and phrases:
simple set, Poonen, Hilbert's tenth problem for the rational numbers.
Received: 10.05.2010
Citation:
M. Davis, “Representation theorems for r.e. sets and a conjecture related to Poonen's larges subring of $\mathbb Q$”, Studies in number theory. Part 10, Zap. Nauchn. Sem. POMI, 377, POMI, St. Petersburg, 2010, 50–54; J. Math. Sci. (N. Y.), 171:6 (2010), 728–730
Linking options:
https://www.mathnet.ru/eng/znsl3813 https://www.mathnet.ru/eng/znsl/v377/p50
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Abstract page: | 139 | Full-text PDF : | 49 | References: | 46 |
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