{"id":"https://openalex.org/W4254972006","doi":"https://doi.org/10.3233/fi-2010-255","title":"Algebraic Ordinals","display_name":"Algebraic Ordinals","publication_year":2010,"publication_date":"2010-05-01","ids":{"openalex":"https://openalex.org/W4254972006","doi":"https://doi.org/10.3233/fi-2010-255"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2010-255","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2010-255","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050710436","display_name":"Stephen L. Bloom","orcid":null},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen L. Bloom","raw_affiliation_strings":["Department of Computer Science, Stevens Institute of\r\t\t\t Technology, Hoboken, NJ, USA. E-mail: bloom@cs.stevens.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Stevens Institute of\r\t\t\t Technology, Hoboken, NJ, USA. E-mail: bloom@cs.stevens.edu","institution_ids":["https://openalex.org/I108468826"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017293831","display_name":"Zolt\u00e1n \u00c9sik","orcid":null},"institutions":[{"id":"https://openalex.org/I227486990","display_name":"University of Szeged","ror":"https://ror.org/01pnej532","country_code":"HU","type":"education","lineage":["https://openalex.org/I227486990"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Zoltan \u00c9sik","raw_affiliation_strings":["Department of Informatics, University of Szeged,\r\t\t\t Szeged, Hungary. E-mail: ze@inf.u-szeged.hu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Szeged,\r\t\t\t Szeged, Hungary. E-mail: ze@inf.u-szeged.hu","institution_ids":["https://openalex.org/I227486990"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3828,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.92640923,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"99","issue":"4","first_page":"383","last_page":"407"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.4129999876022339,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.4129999876022339,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6010494232177734},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.45399177074432373},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41997572779655457},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38756290078163147},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3411558270454407},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10835283994674683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6010494232177734},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45399177074432373},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41997572779655457},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38756290078163147},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3411558270454407},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10835283994674683}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2010-255","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2010-255","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":{"An":[0],"algebraic":[1,21,42,48],"tree":[2,22],"T":[3,23],"is":[4,24,35,40],"one":[5],"determined":[6],"by":[7,27],"a":[8],"finite":[9],"system":[10],"of":[11,19],"fixed":[12],"point":[13],"equations.":[14],"The":[15],"frontier":[16],"Fr(T":[17],")":[18],"an":[20,41],"linearly":[25],"ordered":[26],"the":[28,47,52],"lexicographic":[29],"order":[30,38],"<\u2113":[31],"If":[32],"(Fr(T)":[33],"<\u2113)":[34],"well-ordered,":[36],"its":[37],"type":[39],"ordinal.":[43],"We":[44],"prove":[45],"that":[46],"ordinals":[49,53],"are":[50],"exactly":[51],"less":[54],"than":[55],"\u03c9":[56],"$^{ω}$":[57,58],".":[59]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2022-05-12T00:00:00"}