{"id":"https://openalex.org/W2129772766","doi":"https://doi.org/10.1142/s0129054111008155","title":"ALGEBRAIC LINEAR ORDERINGS","display_name":"ALGEBRAIC LINEAR ORDERINGS","publication_year":2011,"publication_date":"2011-02-01","ids":{"openalex":"https://openalex.org/W2129772766","doi":"https://doi.org/10.1142/s0129054111008155","mag":"2129772766"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054111008155","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054111008155","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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":"S. L. BLOOM","raw_affiliation_strings":["Dept. of Computer Science, Stevens Institute of Technology, Hoboken, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science, Stevens Institute of Technology, Hoboken, NJ, USA","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":"Z. \u00c9SIK","raw_affiliation_strings":["Dept. of Informatics, University of Szeged, Szeged, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Informatics, University of Szeged, Szeged, Hungary","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":4.7451,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.95010992,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"22","issue":"02","first_page":"491","last_page":"515"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9970999956130981,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9970999956130981,"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/T11567","display_name":"semigroups and automata theory","score":0.9947999715805054,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9919999837875366,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7817920446395874},{"id":"https://openalex.org/keywords/algebraic-cycle","display_name":"Algebraic cycle","score":0.5745241641998291},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5599384903907776},{"id":"https://openalex.org/keywords/algebraic-extension","display_name":"Algebraic extension","score":0.5513241291046143},{"id":"https://openalex.org/keywords/dimension-of-an-algebraic-variety","display_name":"Dimension of an algebraic variety","score":0.5474473237991333},{"id":"https://openalex.org/keywords/algebraic-element","display_name":"Algebraic element","score":0.513328492641449},{"id":"https://openalex.org/keywords/function-field-of-an-algebraic-variety","display_name":"Function field of an algebraic variety","score":0.5016059875488281},{"id":"https://openalex.org/keywords/algebraic-theory","display_name":"Algebraic theory","score":0.4871025085449219},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.42355093359947205},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.41553518176078796},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3886282444000244},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34872788190841675}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7817920446395874},{"id":"https://openalex.org/C199793520","wikidata":"https://www.wikidata.org/wiki/Q4723996","display_name":"Algebraic cycle","level":3,"score":0.5745241641998291},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5599384903907776},{"id":"https://openalex.org/C89290136","wikidata":"https://www.wikidata.org/wiki/Q550791","display_name":"Algebraic extension","level":5,"score":0.5513241291046143},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.5474473237991333},{"id":"https://openalex.org/C173832452","wikidata":"https://www.wikidata.org/wiki/Q162608","display_name":"Algebraic element","level":5,"score":0.513328492641449},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.5016059875488281},{"id":"https://openalex.org/C2779782106","wikidata":"https://www.wikidata.org/wiki/Q4724020","display_name":"Algebraic theory","level":3,"score":0.4871025085449219},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.42355093359947205},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.41553518176078796},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3886282444000244},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34872788190841675},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054111008155","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054111008155","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W11531364","https://openalex.org/W1541737641","https://openalex.org/W1553920270","https://openalex.org/W1608752509","https://openalex.org/W1963646041","https://openalex.org/W1980091988","https://openalex.org/W1991735660","https://openalex.org/W1998523218","https://openalex.org/W2007098021","https://openalex.org/W2025670714","https://openalex.org/W2050407768","https://openalex.org/W2061786858","https://openalex.org/W2064143133","https://openalex.org/W2080801189","https://openalex.org/W2116509046","https://openalex.org/W2912108314","https://openalex.org/W4212983671","https://openalex.org/W4254972006","https://openalex.org/W4302339081","https://openalex.org/W4403143202"],"related_works":["https://openalex.org/W4233049353","https://openalex.org/W3090789507","https://openalex.org/W4256397181","https://openalex.org/W1502419693","https://openalex.org/W635989923","https://openalex.org/W1984537908","https://openalex.org/W4205696848","https://openalex.org/W1502425857","https://openalex.org/W2129772766","https://openalex.org/W436532147"],"abstract_inverted_index":{"An":[0],"algebraic":[1,41,57,63,74,94,105,116,129],"linear":[2,23,42,50,71,95,117],"ordering":[3,51,72,86,96,118],"is":[4,73,97,103,119],"a":[5,12,36,70,88,98],"component":[6],"of":[7,11,21,52,55,62,87,113],"the":[8,17,27,31,49,53,67,84,93,110,128],"initial":[9],"solution":[10],"first-order":[13],"recursion":[14],"scheme":[15],"over":[16],"continuous":[18],"categorical":[19],"algebra":[20],"countable":[22],"orderings":[24,43],"equipped":[25],"with":[26],"sum":[28],"operation":[29],"and":[30,76],"constant":[32],"1.":[33],"Due":[34],"to":[35,48],"general":[37],"Mezei-Wright":[38],"type":[39,102],"result,":[40],"are":[44,131],"exactly":[45,132],"those":[46,133],"isomorphic":[47],"leaves":[54],"an":[56,104],"tree.":[58],"Using":[59],"Courcelle's":[60],"characterization":[61],"trees,":[64],"we":[65],"obtain":[66],"fact":[68],"that":[69,109,127],"if":[75,78],"only":[77],"it":[79],"can":[80],"be":[81],"represented":[82],"as":[83],"lexicographic":[85],"deterministic":[89],"context-free":[90],"language.":[91],"When":[92],"well-ordering,":[99],"its":[100],"order":[101],"ordinal.":[106],"We":[107],"prove":[108],"Hausdorff":[111],"rank":[112],"any":[114],"scattered":[115],"less":[120,134],"than":[121,135],"\u03c9":[122,123,136,137,138],".":[124,139],"It":[125],"follows":[126],"ordinals":[130]},"counts_by_year":[{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
