{"id":"https://openalex.org/W2124073211","doi":"https://doi.org/10.2307/2273359","title":"Two-dimensional partial orderings: Recursive model theory","display_name":"Two-dimensional partial orderings: Recursive model theory","publication_year":1980,"publication_date":"1980-03-01","ids":{"openalex":"https://openalex.org/W2124073211","doi":"https://doi.org/10.2307/2273359","mag":"2124073211"},"language":"en","primary_location":{"id":"doi:10.2307/2273359","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273359","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal 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/A5086277174","display_name":"Alfred B. Manaster","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alfred B. Manaster","raw_affiliation_strings":["University of California at San Diego, La Jolla, CA 92037"],"affiliations":[{"raw_affiliation_string":"University of California at San Diego, La Jolla, CA 92037","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000807983","display_name":"Joseph G. Rosenstein","orcid":null},"institutions":[{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]},{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joseph G. Rosenstein","raw_affiliation_strings":["Institute of Advanced Study, Princeton, NJ 08540","Rutgers University, New Brunswick, NJ 08903"],"affiliations":[{"raw_affiliation_string":"Institute of Advanced Study, Princeton, NJ 08540","institution_ids":["https://openalex.org/I40036882"]},{"raw_affiliation_string":"Rutgers University, New Brunswick, NJ 08903","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086277174"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":2.2939,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.89912933,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"1","first_page":"121","last_page":"132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9993000030517578,"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/T11567","display_name":"semigroups and automata theory","score":0.9993000030517578,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9926999807357788,"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":0.9922000169754028,"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/lexicographical-order","display_name":"Lexicographical order","score":0.7288108468055725},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6940044164657593},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.6444382071495056},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6442347168922424},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.578763484954834},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.5077370405197144},{"id":"https://openalex.org/keywords/partial-function","display_name":"Partial function","score":0.4766312837600708},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.45796066522598267},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4325265884399414},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.416892409324646},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.41300612688064575}],"concepts":[{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.7288108468055725},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6940044164657593},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.6444382071495056},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6442347168922424},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.578763484954834},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.5077370405197144},{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.4766312837600708},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.45796066522598267},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4325265884399414},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.416892409324646},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.41300612688064575},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273359","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273359","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183740515","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183740515","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":12,"referenced_works":["https://openalex.org/W1554860413","https://openalex.org/W2003367401","https://openalex.org/W2065461197","https://openalex.org/W2068654529","https://openalex.org/W2090451983","https://openalex.org/W2131443763","https://openalex.org/W2154635726","https://openalex.org/W2318940310","https://openalex.org/W2325654786","https://openalex.org/W4211184603","https://openalex.org/W4246804796","https://openalex.org/W6828398953"],"related_works":["https://openalex.org/W2030040278","https://openalex.org/W2949719962","https://openalex.org/W4292861741","https://openalex.org/W4206375802","https://openalex.org/W2469510813","https://openalex.org/W2180082329","https://openalex.org/W2041561968","https://openalex.org/W4244805628","https://openalex.org/W2152953809","https://openalex.org/W2058313567"],"abstract_inverted_index":{"In":[0,171],"this":[1],"paper":[2,6],"and":[3,20,38,136,144,177,187,225,227,247],"the":[4,15,21,100,104,107,114,159,162,206],"companion":[5],"[9]":[7],"we":[8],"describe":[9],"a":[10,43,179,195,209,232,240,244,256],"number":[11,210],"of":[12,17,23,29,60,103,161,166,197,208,211,234,254],"contrasts":[13],"between":[14],"theory":[16,22],"linear":[18,58,101],"orderings":[19,33,59,165,203,237],"two-dimensional":[24],"partial":[25,32,44,181,202,236,241],"orderings.":[26],"The":[27],"notion":[28],"dimensionality":[30],"for":[31,95],"was":[34],"introduced":[35],"by":[36,175,222],"Dushnik":[37,176],"Miller":[39],"[3],":[40],"who":[41],"defined":[42],"ordering":[45,102,116,182,242],"\u3008":[46,63,68,74,128],"A,":[47,64,69,75],"R":[48,81],"\u3009":[49,72,78,123],"to":[50],"be":[51,192],"n":[52,57,77,92,184,199],"-dimensional":[53,185],"if":[54,97,135,138,186,189,246,249],"there":[55],"are":[56],"A":[61,216],",":[62,120,131,134],"L":[65,70,76,83,86,91],"1":[66,84,119,122,140,146],"\u3009,":[67],"2":[71,87,130,133,143,149],"\u2026,":[73],"such":[79,238],"that":[80,239],"=":[82],"\u2229":[85,88,90],"\u2026":[89],".":[93,170,200],"Thus,":[94],"example,":[96],"Q":[98,110,112,125,127,155,157,167,169,198],"is":[99,151,158,183,243],"rationals,":[105],"then":[106],"(rational)":[108],"plane":[109],"\u00d7":[111,126,156,168],"with":[113],"product":[115],"(\u3008":[117],"x":[118,129,139,142],"y":[121,132,145,148],"\u2264":[124,141,147,154],"only":[137,188,248],")":[150],"2-dimensional,":[152],"since":[153],"intersection":[160],"two":[163],"lexicographic":[164],"fact,":[172],"as":[173,194,255],"shown":[174],"Miller,":[178],"countable":[180],"it":[190,250],"can":[191],"embedded":[193],"subordering":[196],"Two-dimensional":[201],"have":[204],"attracted":[205],"attention":[207],"combinatorialists":[212],"in":[213],"recent":[214],"years.":[215],"basis":[217],"result":[218],"recently":[219],"obtained,":[220],"independently,":[221],"Kelly":[223],"[7]":[224],"Trotter":[226],"Moore":[228],"[10],":[229],"describes":[230],"explicitly":[231],"collection":[233],"finite":[235],"2dpo":[245],"contains":[251],"no":[252],"element":[253],"subordering.":[257]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}