{"id":"https://openalex.org/W2003367401","doi":"https://doi.org/10.2307/2273360","title":"Two-dimensional partial orderings: Undecidability","display_name":"Two-dimensional partial orderings: Undecidability","publication_year":1980,"publication_date":"1980-03-01","ids":{"openalex":"https://openalex.org/W2003367401","doi":"https://doi.org/10.2307/2273360","mag":"2003367401"},"language":"en","primary_location":{"id":"doi:10.2307/2273360","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273360","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, San Diego, La Jolla, CA 92037"],"affiliations":[{"raw_affiliation_string":"University of California, 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":2.8674,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.90953493,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"1","first_page":"133","last_page":"143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9997000098228455,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9997000098228455,"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":0.996999979019165,"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/T12029","display_name":"DNA and Biological Computing","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.9361916780471802},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.789242148399353},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7132904529571533},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6317110061645508},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5480118989944458},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5431737899780273},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44984883069992065},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.41778916120529175},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.4105868935585022},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.16776826977729797},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14442497491836548}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.9361916780471802},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.789242148399353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7132904529571533},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6317110061645508},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5480118989944458},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5431737899780273},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44984883069992065},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.41778916120529175},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.4105868935585022},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.16776826977729797},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14442497491836548},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273360","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273360","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/1183740516","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183740516","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1511526676","https://openalex.org/W1580523149","https://openalex.org/W1580868918","https://openalex.org/W1985156927","https://openalex.org/W2043620450","https://openalex.org/W2080896750","https://openalex.org/W2104414147","https://openalex.org/W2124073211","https://openalex.org/W2334611908","https://openalex.org/W4241710558","https://openalex.org/W4246584577","https://openalex.org/W6661438794"],"related_works":["https://openalex.org/W2972379433","https://openalex.org/W1501430220","https://openalex.org/W2989332944","https://openalex.org/W2021891065","https://openalex.org/W2583549044","https://openalex.org/W2119045600","https://openalex.org/W2584984136","https://openalex.org/W1542027783","https://openalex.org/W4234189135","https://openalex.org/W2170336571"],"abstract_inverted_index":{"In":[0],"this":[1,21,269],"paper":[2],"we":[3,50],"examine":[4],"the":[5,12,23,31,42,61,66,73,81,108,119,131,134,169,172,188,227,240,249],"class":[6,24,32,43],"of":[7,14,25,33,44,60,68,75,83,110,121,136,152,171,174,229,242,251,271],"two-dimensional":[8],"partial":[9,35,137,175],"orderings":[10,36,123,138,176],"from":[11,20,80,158,248,268],"perspective":[13,22],"undecidability.":[15],"We":[16],"shall":[17,51],"see":[18],"that":[19,118,150,207,226,239],"2dpo's":[26,69,76,189],"is":[27,70,77,92,96,113,116,124,155,232,245],"more":[28],"similar":[29],"to":[30,38,58,143,222,235,266],"all":[34,45],"than":[37],"its":[39,159],"one-dimensional":[40],"subclass,":[41],"linear":[46,122],"orderings.":[47],"More":[48],"specifically,":[49],"describe":[52],"an":[53],"argument":[54,220],"which":[55,95,102],"lends":[56],"itself":[57],"proofs":[59],"following":[62],"four":[63],"results:":[64],"(A)":[65,208],"theory":[67,74,109,120,228,241],"undecidable:":[71],"(B)":[72,182,210],"recursively":[78,156,246],"inseparable":[79,157,247],"set":[82,250],"sentences":[84,252],"refutable":[85,161,253],"in":[86,98,187,254],"some":[87,99,255],"finite":[88,256],"2dpo;":[89],"(C)":[90,260],"there":[91],"a":[93,217],"sentence":[94],"true":[97],"2dpo":[100],"but":[101],"has":[103],"no":[104],"recursive":[105],"model;":[106],"(D)":[107,262],"planar":[111,191],"lattices":[112,140,178],"undecidable.":[114],"It":[115],"known":[117],"decidable":[125],"(Lauchli":[126],"and":[127,139,149,177,183,190,209,234,261],"Leonard":[128],"[4]).":[129],"On":[130],"other":[132],"hand,":[133],"theories":[135,154,173],"were":[141],"shown":[142,164],"be":[144,202,213],"undecidable":[145,233],"by":[146,165,180,196,215],"Tarski":[147],"[14],":[148],"each":[151],"these":[153],"finitely":[160],"statements":[162],"was":[163],"Taitslin":[166],"[13].":[167],"Thus,":[168],"complexity":[170],"is,":[179],"(A),":[181],"(D),":[184],"already":[185],"reflected":[186],"lattices.":[192],"As":[193],"pointed":[194],"out":[195],"J.":[197],"Schmerl,":[198],"bipartite":[199,230,243,257],"graphs":[200,231,244],"can":[201],"coded":[203],"into":[204],"2dpo's,":[205],"so":[206],"could":[211],"also":[212],"obtained":[214],"applying":[216],"Rabin-Scott":[218],"style":[219],"[9]":[221],"Rogers'":[223],"result":[224,237],"[11]":[225],"Lavrov's":[236],"[5]":[238],"graph.":[258],"(However,":[259],"do":[263],"not":[264],"seem":[265],"follow":[267],"type":[270],"argument.)":[272]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
