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http://hdl.handle.net/11320/6835
Pełny rekord metadanych
Pole DC | Wartość | Język |
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dc.contributor.author | Pąk, Karol | - |
dc.date.accessioned | 2018-08-20T06:41:53Z | - |
dc.date.available | 2018-08-20T06:41:53Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Formalized Mathematics, Volume 26, Issue 1, Pages 81–90 | - |
dc.identifier.issn | 1426-2630 | - |
dc.identifier.uri | http://hdl.handle.net/11320/6835 | - |
dc.description.abstract | In this article, we define Diophantine sets using the Mizar formalism. We focus on selected properties of multivariate polynomials, i.e., functions of several variables to show finally that the class of Diophantine sets is closed with respect to the operations of union and intersection. This article is the next in a series [1], [5] aiming to formalize the proof of Matiyasevich’s negative solution of Hilbert’s tenth problem. | - |
dc.language.iso | en | - |
dc.publisher | DeGruyter Open | - |
dc.subject | Hilbert’s 10th problem | - |
dc.subject | Pell’s equation | - |
dc.subject | multivariate polynomials | - |
dc.title | Diophantine sets. Preliminaries | - |
dc.type | Article | - |
dc.identifier.doi | 10.2478/forma-2018-0007 | - |
dc.description.Affiliation | Institute of Informatics, University of Białystok, Poland | - |
dc.description.references | Marcin Acewicz and Karol Pąk. Pell’s equation. Formalized Mathematics, 25(3):197–204, 2017. doi:10.1515/forma-2017-0019. | - |
dc.description.references | Zofia Adamowicz and Paweł Zbierski. Logic of Mathematics: A Modern Course of Classical Logic. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Wiley-Interscience, 1997. | - |
dc.description.references | Czesław Byliński. Some properties of restrictions of finite sequences. Formalized Mathematics, 5(2):241–245, 1996. | - |
dc.description.references | Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1. | - |
dc.description.references | Karol Pąk. The Matiyasevich theorem. Preliminaries. Formalized Mathematics, 25(4): 315–322, 2017. doi:10.1515/forma-2017-0029. | - |
dc.description.references | Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Formalized Mathematics, 9(1):95–110, 2001. | - |
dc.description.references | Craig Smorynski. Logical Number Theory I, An Introduction. Universitext. Springer-Verlag Berlin Heidelberg, 1991. ISBN 978-3-642-75462-3. | - |
dc.description.references | Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825–829, 2001. | - |
dc.identifier.eissn | 1898-9934 | - |
dc.description.volume | 26 | - |
dc.description.issue | 1 | - |
dc.description.firstpage | 81 | - |
dc.description.lastpage | 90 | - |
dc.identifier.citation2 | Formalized Mathematics | - |
Występuje w kolekcji(ach): | Artykuły naukowe (WInf) Formalized Mathematics, 2018, Volume 26, Issue 1 |
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