{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T11:27:27Z","timestamp":1777462047865,"version":"3.51.4"},"reference-count":10,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,9,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>\n                    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,\n                    <jats:italic>Properties of Order and Equality<\/jats:italic>\n                    of John Conway\u2019s 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.\n                  <\/jats:p>","DOI":"10.2478\/forma-2023-0019","type":"journal-article","created":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T13:42:34Z","timestamp":1704116554000},"page":"205-213","source":"Crossref","is-referenced-by-count":5,"title":["Integration of Game Theoretic and Tree Theoretic Approaches to Conway Numbers"],"prefix":"10.2478","volume":"31","author":[{"given":"Karol","family":"P\u0105k","sequence":"first","affiliation":[{"name":"Faculty of Computer Science , University of Bia\u0142ystok , Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,12,31]]},"reference":[{"key":"2026042801385070931_j_forma-2023-0019_ref_001","unstructured":"Maan T. Alabdullah, Essam El-Seidy, and Neveen S. Morcos. On numbers and games. International Journal of Scientific and Engineering Research, 11:510\u2013517, February 2020."},{"key":"2026042801385070931_j_forma-2023-0019_ref_002","unstructured":"Norman L. Alling. Foundations of Analysis Over Surreal Number Fields. Number 141 in Annals of Discrete Mathematics. North-Holland, 1987. ISBN 9780444702265."},{"key":"2026042801385070931_j_forma-2023-0019_ref_003","unstructured":"John Horton Conway. On Numbers and Games. A K Peters Ltd., Natick, MA, second edition, 2001. ISBN 1-56881-127-6."},{"key":"2026042801385070931_j_forma-2023-0019_ref_004","doi-asserted-by":"crossref","unstructured":"Philip Ehrlich. Conway names, the simplicity hierarchy and the surreal number tree. Journal of Logic and Analysis, 3(1):1\u201326, 2011. doi:10.4115\/jla.2011.3.1.","DOI":"10.4115\/jla.2011.3.1"},{"key":"2026042801385070931_j_forma-2023-0019_ref_005","doi-asserted-by":"crossref","unstructured":"Philip Ehrlich. The absolute arithmetic continuum and the unification of all numbers great and small. The Bulletin of Symbolic Logic, 18(1):1\u201345, 2012. doi:10.2178\/bsl\/1327328438.","DOI":"10.2178\/bsl\/1327328438"},{"key":"2026042801385070931_j_forma-2023-0019_ref_006","doi-asserted-by":"crossref","unstructured":"Philp Ehrlich. Number systems with simplicity hierarchies: A generalization of Conway\u2019s theory of surreal numbers. Journal of Symbolic Logic, 66(3):1231\u20131258, 2001. doi:10.2307\/2695104.","DOI":"10.2307\/2695104"},{"key":"2026042801385070931_j_forma-2023-0019_ref_007","doi-asserted-by":"crossref","unstructured":"Sebastian Koch. Natural addition of ordinals. Formalized Mathematics, 27(2):139\u2013152, 2019. doi:10.2478\/forma-2019-0015.","DOI":"10.2478\/forma-2019-0015"},{"key":"2026042801385070931_j_forma-2023-0019_ref_008","unstructured":"Karol P\u0105k. Stirling numbers of the second kind. Formalized Mathematics, 13(2):337\u2013345, 2005."},{"key":"2026042801385070931_j_forma-2023-0019_ref_009","doi-asserted-by":"crossref","unstructured":"Karol P\u0105k. Conway numbers \u2013 formal introduction. Formalized Mathematics, 31(1): 193\u2013203, 2023. doi:10.2478\/forma-2023-0018.","DOI":"10.2478\/forma-2023-0018"},{"key":"2026042801385070931_j_forma-2023-0019_ref_010","doi-asserted-by":"crossref","unstructured":"Dierk Schleicher and Michael Stoll. An introduction to Conway\u2019s games and numbers. Moscow Mathematical Journal, 6:359\u2013388, 2006. doi:10.17323\/1609-4514-2006-6-2-359-388.","DOI":"10.17323\/1609-4514-2006-6-2-359-388"}],"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/reference-global.com\/pdf\/10.2478\/forma-2023-0019","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T13:16:14Z","timestamp":1777382174000},"score":1,"resource":{"primary":{"URL":"https:\/\/reference-global.com\/article\/10.2478\/forma-2023-0019"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,1]]},"references-count":10,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,12,31]]},"published-print":{"date-parts":[[2023,9,1]]}},"alternative-id":["10.2478\/forma-2023-0019"],"URL":"https:\/\/doi.org\/10.2478\/forma-2023-0019","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,1]]}}}