Integration of Game Theoretic and Tree Theoretic Approaches to Conway Numbers

Pole DC	Wartość	Język
dc.contributor.author	Pąk, Karol	-
dc.date.accessioned	2024-01-25T11:54:57Z	-
dc.date.available	2024-01-25T11:54:57Z	-
dc.date.issued	2023	-
dc.identifier.citation	Formalized Mathematics, Volume 31, Issue 1, Pages 205-213	pl
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/15857	-
dc.description.abstract	In this article, we develop our formalised concept of Conway numbers as outlined in [9]. We focus mainly pre-order properties, birthday arithmetic contained in the Chapter 1, Properties of Order and Equality of John Conway’s seminal book. We also propose a method for the selection of class representatives respecting the relation defined by the pre-ordering in order to facilitate combining the results obtained for the original and tree-theoretic definitions of Conway numbers.	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.subject	Mizar	pl
dc.title	Integration of Game Theoretic and Tree Theoretic Approaches to Conway Numbers	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-2023-0019	-
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	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	Philip Ehrlich. Conway names, the simplicity hierarchy and the surreal number tree. Journal of Logic and Analysis, 3(1):1–26, 2011. doi:10.4115/jla.2011.3.1.	pl
dc.description.references	Philip Ehrlich. The absolute arithmetic continuum and the unification of all numbers great and small. The Bulletin of Symbolic Logic, 18(1):1–45, 2012. doi:10.2178/bsl/1327328438.	pl
dc.description.references	Philp Ehrlich. Number systems with simplicity hierarchies: A generalization of Conway’s theory of surreal numbers. Journal of Symbolic Logic, 66(3):1231–1258, 2001. doi:10.2307/2695104.	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. Stirling numbers of the second kind. Formalized Mathematics, 13(2):337–345, 2005.	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	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	205	pl
dc.description.lastpage	213	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

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