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http://hdl.handle.net/11320/15858Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Pąk, Karol | - |
| dc.date.accessioned | 2024-01-25T12:36:22Z | - |
| dc.date.available | 2024-01-25T12:36:22Z | - |
| dc.date.issued | 2023 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 31, Issue 1, Pages 215-228 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/15858 | - |
| dc.description.abstract | Conway’s introduction to algebraic operations on surreal numbers with a rather simple definition. However, he combines recursion with Conway’s induction on surreal numbers, more formally he combines transfinite induction-recursion with the properties of proper classes, which is difficult to introduce formally. This article represents a further step in our ongoing efforts to investigate the possibilities offered by Mizar with Tarski-Grothendieck set theory [4] to introduce the algebraic structure of Conway numbers and to prove their ring character. | pl |
| dc.language.iso | en | pl |
| dc.publisher | DeGruyter Open | pl |
| dc.rights | Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) | pl |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/3.0/ | pl |
| dc.subject | surreal numbers | pl |
| dc.subject | Conway’s game | pl |
| dc.title | The Ring of Conway Numbers in Mizar | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2022 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 3.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2023-0020 | - |
| dc.description.Affiliation | Faculty of Computer Science, University of Białystok, Poland | pl |
| dc.description.references | Maan T. Alabdullah, Essam El-Seidy, and Neveen S. Morcos. On numbers and games. International Journal of Scientific and Engineering Research, 11:510–517, February 2020. | pl |
| dc.description.references | Norman L. Alling. Foundations of Analysis Over Surreal Number Fields. Number 141 in Annals of Discrete Mathematics. North-Holland, 1987. ISBN 9780444702265. | pl |
| dc.description.references | Heinz Bachmann. Transfinite Zahlen. Ergebnisse der Mathematik und ihrer Grenzgebiete, (1). Springer, Berlin, 2., neubearb. aufl. edition, 1967. | pl |
| dc.description.references | Chad E. Brown and Karol Pąk. A tale of two set theories. In Cezary Kaliszyk, Edwin Brady, Andrea Kohlhase, and Claudio Sacerdoti Coen, editors, Intelligent Computer Mathematics – 12th International Conference, CICM 2019, CIIRC, Prague, Czech Republic, July 8-12, 2019, Proceedings, volume 11617 of Lecture Notes in Computer Science, pages 44–60. Springer, 2019. doi:10.1007/978-3-030-23250-4_4. | pl |
| dc.description.references | John Horton Conway. On Numbers and Games. A K Peters Ltd., Natick, MA, second edition, 2001. ISBN 1-56881-127-6. | pl |
| dc.description.references | Oliver Deiser. Einführung in die Mengenlehre: die Mengenlehre Georg Cantors und ihre Axiomatisierung durch Ernst Zermelo. Springer, Berlin, 2., verb. und erw. aufl. edition, 2004. ISBN 3-540-20401-6. | pl |
| dc.description.references | Sebastian Koch. Natural addition of ordinals. Formalized Mathematics, 27(2):139–152, 2019. doi:10.2478/forma-2019-0015. | pl |
| dc.description.references | Karol Pąk. Conway numbers – formal introduction. Formalized Mathematics, 31(1): 193–203, 2023. doi:10.2478/forma-2023-0018. | pl |
| dc.description.references | Karol Pąk. Integration of game theoretic and tree theoretic approaches to Conway numbers. Formalized Mathematics, 31(1):205–213, 2023. doi:10.2478/forma-2023-0019. | pl |
| dc.description.references | Dierk Schleicher and Michael Stoll. An introduction to Conway’s games and numbers. Moscow Mathematical Journal, 6:359–388, 2006. doi:10.17323/1609-4514-2006-6-2-359-388. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 31 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 215 | pl |
| dc.description.lastpage | 228 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| dc.identifier.orcid | 0000-0002-7099-1669 | - |
| Występuje w kolekcji(ach): | Artykuły naukowe (WInf) Formalized Mathematics, 2023, Volume 31, Issue 1 | |
Pliki w tej pozycji:
| Plik | Opis | Rozmiar | Format | |
|---|---|---|---|---|
| The-Ring-of-Conway-Numbers-in-Mizar.pdf | 304,48 kB | Adobe PDF | Otwórz |
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