{"id":"https://openalex.org/W1996647670","doi":"https://doi.org/10.2178/bsl/1174668219","title":"On the Equimorphism Types of Linear Orderings","display_name":"On the Equimorphism Types of Linear Orderings","publication_year":2007,"publication_date":"2007-03-01","ids":{"openalex":"https://openalex.org/W1996647670","doi":"https://doi.org/10.2178/bsl/1174668219","mag":"1996647670"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1174668219","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1174668219","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of Symbolic Logic","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/A5033772009","display_name":"Antonio Montalb\u00e1n","orcid":"https://orcid.org/0000-0002-5068-1444"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Antonio Montalb\u00e1n","raw_affiliation_strings":["Department of Mathematics, University of Chicago, Chicago, IL, USAE-mail:","University-of Chicago"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Chicago, Chicago, IL, USAE-mail:","institution_ids":["https://openalex.org/I40347166","https://openalex.org/I39422238"]},{"raw_affiliation_string":"University-of Chicago","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033772009"],"corresponding_institution_ids":["https://openalex.org/I39422238","https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":1.1217,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.77452516,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"13","issue":"1","first_page":"71","last_page":"99"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":1.0,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":1.0,"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/T11567","display_name":"semigroups and automata theory","score":0.9951000213623047,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9891999959945679,"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":0.7902655005455017},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.7711609601974487},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.6453578472137451},{"id":"https://openalex.org/keywords/reverse-mathematics","display_name":"Reverse mathematics","score":0.575287938117981},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5711710453033447},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.5341365337371826},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44716936349868774},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.44401922821998596},{"id":"https://openalex.org/keywords/linear-extension","display_name":"Linear extension","score":0.41554513573646545},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3489990830421448},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3370705544948578},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32494521141052246},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.2812191843986511},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15118208527565002},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.08069473505020142}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7902655005455017},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.7711609601974487},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.6453578472137451},{"id":"https://openalex.org/C127753061","wikidata":"https://www.wikidata.org/wiki/Q2005236","display_name":"Reverse mathematics","level":3,"score":0.575287938117981},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5711710453033447},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.5341365337371826},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44716936349868774},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.44401922821998596},{"id":"https://openalex.org/C129393996","wikidata":"https://www.wikidata.org/wiki/Q6553442","display_name":"Linear extension","level":3,"score":0.41554513573646545},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3489990830421448},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3370705544948578},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32494521141052246},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.2812191843986511},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15118208527565002},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.08069473505020142},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/bsl/1174668219","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1174668219","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1174668219","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1174668219","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W6616102","https://openalex.org/W9430111","https://openalex.org/W79809236","https://openalex.org/W198811082","https://openalex.org/W213603931","https://openalex.org/W264938754","https://openalex.org/W395347316","https://openalex.org/W562130350","https://openalex.org/W968309248","https://openalex.org/W1495615244","https://openalex.org/W1505964586","https://openalex.org/W1513955923","https://openalex.org/W1538838225","https://openalex.org/W1539702044","https://openalex.org/W1556453281","https://openalex.org/W1561798411","https://openalex.org/W1964766966","https://openalex.org/W1974315792","https://openalex.org/W1978413491","https://openalex.org/W1981473293","https://openalex.org/W1982821787","https://openalex.org/W1994073383","https://openalex.org/W1996932891","https://openalex.org/W1999737391","https://openalex.org/W1999947171","https://openalex.org/W2017855260","https://openalex.org/W2018765574","https://openalex.org/W2028592975","https://openalex.org/W2028858836","https://openalex.org/W2034581612","https://openalex.org/W2047865735","https://openalex.org/W2052953762","https://openalex.org/W2056414301","https://openalex.org/W2057398815","https://openalex.org/W2065144039","https://openalex.org/W2067474877","https://openalex.org/W2070851509","https://openalex.org/W2080426944","https://openalex.org/W2081624356","https://openalex.org/W2098052203","https://openalex.org/W2104452294","https://openalex.org/W2138899395","https://openalex.org/W2148962283","https://openalex.org/W2279468699","https://openalex.org/W2316932045","https://openalex.org/W2319602497","https://openalex.org/W2329685449","https://openalex.org/W2551720480","https://openalex.org/W2736186402","https://openalex.org/W4232277851","https://openalex.org/W4240833632","https://openalex.org/W4245060240","https://openalex.org/W4296119740","https://openalex.org/W6655199249","https://openalex.org/W6741189996"],"related_works":["https://openalex.org/W1507261115","https://openalex.org/W1592365926","https://openalex.org/W2499765358","https://openalex.org/W643812077","https://openalex.org/W2349728712","https://openalex.org/W2519278145","https://openalex.org/W2964292697","https://openalex.org/W2534696914","https://openalex.org/W2078669210","https://openalex.org/W1996647670"],"abstract_inverted_index":{"\u00a71.":[0],"Introduction":[1],".":[2,54],"A":[3],"linear":[4,14,26,63,97,115,165],"ordering":[5,15],"(also":[6],"known":[7],"as":[8,90],"total":[9],"ordering)":[10],"embeds":[11],"into":[12,178],"another":[13],"if":[16,33],"it":[17,142],"is":[18,42,66,75,131],"isomorphic":[19],"to":[20,30,127,138,145,156],"a":[21,101,124,147,157],"subset":[22],"of":[23,59,62,79,93,104,107,114,123,150,159,164],"it.":[24],"Two":[25],"orderings":[27,116,166],"are":[28],"said":[29],"be":[31,36,176],"equimorphic":[32],"they":[34],"can":[35,175],"embedded":[37],"in":[38,110,135],"each":[39],"other.":[40],"This":[41,112,154],"an":[43],"equivalence":[44,50],"relation,":[45],"and":[46,82,167],"we":[47,86],"call":[48],"the":[49,57,70,91,105,120,133,151,162,168],"classes":[51],"equimorphism":[52,60,94],"types":[53,61],"We":[55],"analyze":[56],"structure":[58,109,163],"orderings,":[64,98],"which":[65,99],"partially":[67],"ordered":[68],"by":[69,118],"embeddability":[71,169],"relation.":[72],"Our":[73],"analysis":[74],"mainly":[76],"fromthe":[77],"viewpoints":[78],"Computability":[80],"Theory":[81],"Reverse":[83,136],"Mathematics.":[84],"But":[85],"also":[87],"obtain":[88],"results,":[89],"definition":[92],"invariants":[95],"for":[96],"provide":[100],"better":[102],"understanding":[103,149],"shape":[106],"this":[108,140],"general.":[111],"study":[113],"started":[117],"analyzing":[119],"proof-theoretic":[121],"strength":[122],"theorem":[125],"due":[126],"Jullien":[128],"[Jul69].":[129],"As":[130],"often":[132],"case":[134],"Mathematics,":[137],"solve":[139],"problem":[141],"was":[143],"necessary":[144],"develop":[146],"deeper":[148],"objects":[152],"involved.":[153],"led":[155],"variety":[158],"results":[160,174],"on":[161,171],"relation":[170],"them.":[172],"These":[173],"divided":[177],"three":[179],"groups.":[180]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}