{"id":"https://openalex.org/W4390479513","doi":"https://doi.org/10.2478/forma-2023-0018","title":"Conway Numbers \u2013 Formal Introduction","display_name":"Conway Numbers \u2013 Formal Introduction","publication_year":2023,"publication_date":"2023-09-01","ids":{"openalex":"https://openalex.org/W4390479513","doi":"https://doi.org/10.2478/forma-2023-0018"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2023-0018","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0018","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0018","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/forma-2023-0018","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054103364","display_name":"Karol P\u0105k","orcid":"https://orcid.org/0000-0002-7099-1669"},"institutions":[{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Karol P\u0105k","raw_affiliation_strings":["Faculty of Computer Science , University of Bia\u0142ystok , Poland"],"raw_orcid":"https://orcid.org/0000-0002-7099-1669","affiliations":[{"raw_affiliation_string":"Faculty of Computer Science , University of Bia\u0142ystok , Poland","institution_ids":["https://openalex.org/I245364917"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054103364"],"corresponding_institution_ids":["https://openalex.org/I245364917"],"apc_list":null,"apc_paid":null,"fwci":0.994,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81611211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"31","issue":"1","first_page":"193","last_page":"203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9560999870300293,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13963","display_name":"Organizational Management and Leadership","score":0.9430999755859375,"subfield":{"id":"https://openalex.org/subfields/1405","display_name":"Management of Technology and Innovation"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6704528331756592},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.5183433294296265},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4447508156299591},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.444486141204834},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.358681857585907},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18889373540878296}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6704528331756592},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.5183433294296265},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4447508156299591},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.444486141204834},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.358681857585907},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18889373540878296},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2478/forma-2023-0018","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0018","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0018","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/15856","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/15856","pdf_url":"https://repozytorium.uwb.edu.pl/jspui/bitstream/11320/15856/1/Conway-Numbers-Formal-Introduction.pdf","source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/forma-2023-0018","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0018","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0018","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390479513.pdf"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1485040255","https://openalex.org/W1598110312","https://openalex.org/W2017964937","https://openalex.org/W2058174669","https://openalex.org/W2066252944","https://openalex.org/W2137263714","https://openalex.org/W4252612324","https://openalex.org/W4285326687","https://openalex.org/W4321347226"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Summary":[0],"Surreal":[1],"numbers,":[2],"a":[3],"fascinating":[4],"mathematical":[5],"concept":[6,27],"introduced":[7],"by":[8],"John":[9],"Conway,":[10],"have":[11],"attracted":[12],"considerable":[13],"interest":[14],"due":[15],"to":[16,32],"their":[17],"unique":[18],"properties.":[19],"In":[20],"this":[21],"article,":[22],"we":[23],"formalize":[24],"the":[25,33,38,49,52,57],"basic":[26],"of":[28,40],"surreal":[29,46],"numbers":[30,47],"close":[31],"original":[34],"Conway\u2019s":[35],"convention":[36],"in":[37,51],"field":[39],"combinatorial":[41],"game":[42],"theory.":[43],"We":[44],"define":[45],"with":[48],"pre-order":[50],"Mizar":[53],"system":[54],"which":[55],"satisfy":[56],"following":[58],"condition:":[59],"x":[60,65,72],"\u2a7d":[61],"y":[62,68,76],"iff":[63],"L":[64],"\u226a":[66,74],"{":[67,71],"}":[69,73],"\u039b":[70],"R":[75],".":[77]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}