{"id":"https://openalex.org/W2002993322","doi":"https://doi.org/10.1016/s1571-0661(04)00170-7","title":"Towards Lambda Calculus Order-Incompleteness","display_name":"Towards Lambda Calculus Order-Incompleteness","publication_year":2001,"publication_date":"2001-08-01","ids":{"openalex":"https://openalex.org/W2002993322","doi":"https://doi.org/10.1016/s1571-0661(04)00170-7","mag":"2002993322"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(04)00170-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)00170-7","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/s1571-0661(04)00170-7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064465385","display_name":"Antonino Salibra","orcid":"https://orcid.org/0000-0001-6552-2561"},"institutions":[{"id":"https://openalex.org/I11986463","display_name":"Universit\u00e0 Iuav di Venezia","ror":"https://ror.org/01e6ksd91","country_code":"IT","type":"education","lineage":["https://openalex.org/I11986463"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Antonino Salibra","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 di Venezia Venezia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 di Venezia Venezia, Italy","institution_ids":["https://openalex.org/I11986463"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064465385"],"corresponding_institution_ids":["https://openalex.org/I11986463"],"apc_list":null,"apc_paid":null,"fwci":1.6216,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.86799309,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"50","issue":"2","first_page":"145","last_page":"158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9988999962806702,"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":0.9988999962806702,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9986000061035156,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9948999881744385,"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":0.7300136089324951},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5796748399734497},{"id":"https://openalex.org/keywords/lambda-calculus","display_name":"Lambda calculus","score":0.5293774604797363},{"id":"https://openalex.org/keywords/simply-typed-lambda-calculus","display_name":"Simply typed lambda calculus","score":0.4944155216217041},{"id":"https://openalex.org/keywords/cartesian-closed-category","display_name":"Cartesian closed category","score":0.48348528146743774},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4732249975204468},{"id":"https://openalex.org/keywords/initial-topology","display_name":"Initial topology","score":0.4571712613105774},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.43334275484085083},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36599093675613403},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3358762860298157},{"id":"https://openalex.org/keywords/general-topology","display_name":"General topology","score":0.3198460340499878},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.27747106552124023},{"id":"https://openalex.org/keywords/extension-topology","display_name":"Extension topology","score":0.17110705375671387},{"id":"https://openalex.org/keywords/typed-lambda-calculus","display_name":"Typed lambda calculus","score":0.16053137183189392}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7300136089324951},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5796748399734497},{"id":"https://openalex.org/C135790938","wikidata":"https://www.wikidata.org/wiki/Q242028","display_name":"Lambda calculus","level":2,"score":0.5293774604797363},{"id":"https://openalex.org/C61237538","wikidata":"https://www.wikidata.org/wiki/Q855192","display_name":"Simply typed lambda calculus","level":4,"score":0.4944155216217041},{"id":"https://openalex.org/C171032842","wikidata":"https://www.wikidata.org/wiki/Q1725874","display_name":"Cartesian closed category","level":2,"score":0.48348528146743774},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4732249975204468},{"id":"https://openalex.org/C148420369","wikidata":"https://www.wikidata.org/wiki/Q13416298","display_name":"Initial topology","level":5,"score":0.4571712613105774},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.43334275484085083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36599093675613403},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3358762860298157},{"id":"https://openalex.org/C129089157","wikidata":"https://www.wikidata.org/wiki/Q621550","display_name":"General topology","level":3,"score":0.3198460340499878},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.27747106552124023},{"id":"https://openalex.org/C143913944","wikidata":"https://www.wikidata.org/wiki/Q5421952","display_name":"Extension topology","level":4,"score":0.17110705375671387},{"id":"https://openalex.org/C142156749","wikidata":"https://www.wikidata.org/wiki/Q2607208","display_name":"Typed lambda calculus","level":3,"score":0.16053137183189392},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/s1571-0661(04)00170-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)00170-7","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.23.5325","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.5325","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dsi.unive.it/~salibra/TrueHome/Papers/bohm-salibra.ps","raw_type":"text"},{"id":"pmh:oai:iris.unive.it:10278/8112","is_oa":false,"landing_page_url":"http://hdl.handle.net/10278/8112","pdf_url":null,"source":{"id":"https://openalex.org/S4306402336","display_name":"ARCA (Universit\u00e0 Ca' Foscari Venezia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149461666","host_organization_name":"Ca' Foscari University of Venice","host_organization_lineage":["https://openalex.org/I149461666"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(04)00170-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)00170-7","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W102335877","https://openalex.org/W128738456","https://openalex.org/W159082583","https://openalex.org/W591139221","https://openalex.org/W649174039","https://openalex.org/W1134781054","https://openalex.org/W1488746036","https://openalex.org/W1512478964","https://openalex.org/W1530168704","https://openalex.org/W1563447122","https://openalex.org/W1586379162","https://openalex.org/W1589798016","https://openalex.org/W1607953571","https://openalex.org/W1819331349","https://openalex.org/W1908032243","https://openalex.org/W1967051432","https://openalex.org/W1967121513","https://openalex.org/W1970227944","https://openalex.org/W1974315746","https://openalex.org/W1978856319","https://openalex.org/W1991145017","https://openalex.org/W1993890055","https://openalex.org/W2021900929","https://openalex.org/W2023648368","https://openalex.org/W2038323917","https://openalex.org/W2042426573","https://openalex.org/W2042779906","https://openalex.org/W2054969282","https://openalex.org/W2066155850","https://openalex.org/W2066974910","https://openalex.org/W2068720566","https://openalex.org/W2072459054","https://openalex.org/W2074026916","https://openalex.org/W2075057114","https://openalex.org/W2083955910","https://openalex.org/W2088941870","https://openalex.org/W2088979440","https://openalex.org/W2093541252","https://openalex.org/W2098938409","https://openalex.org/W2104255279","https://openalex.org/W2119310054","https://openalex.org/W2131435036","https://openalex.org/W2132750992","https://openalex.org/W2139772363","https://openalex.org/W2154273644","https://openalex.org/W2318679891","https://openalex.org/W2516185740","https://openalex.org/W2912883082","https://openalex.org/W3127823229","https://openalex.org/W4211265583","https://openalex.org/W4293176479","https://openalex.org/W4299390900","https://openalex.org/W4299453112","https://openalex.org/W6604201901","https://openalex.org/W6824895264"],"related_works":["https://openalex.org/W2119636363","https://openalex.org/W1566334111","https://openalex.org/W1487264664","https://openalex.org/W1592473838","https://openalex.org/W3133088634","https://openalex.org/W1582688644","https://openalex.org/W2942236696","https://openalex.org/W2146437601","https://openalex.org/W2934401054","https://openalex.org/W2114701904"],"abstract_inverted_index":{"After":[0],"Scott,":[1],"mathematical":[2],"models":[3,144,183,199],"of":[4,23,50,62,68,90,102,117,132,155,171,174,180,191,197,200],"the":[5,21,60,63,66,95,118,124,133,148,169,198,201],"type-free":[6],"lambda":[7,34,77,139,175],"calculus":[8,176],"are":[9,145],"constructed":[10],"by":[11,40,94,147],"order":[12,58,61],"theoretic":[13],"methods":[14],"and":[15,83,108,204],"classified":[16],"into":[17],"semantics":[18,173,207],"according":[19],"to":[20,123],"nature":[22],"their":[24],"representable":[25],"functions.":[26],"Selinger":[27],"[48]":[28],"asked":[29],"if":[30],"there":[31,136],"is":[32,37,59,80,92,208],"a":[33,76,129,138,188],"theory":[35,78,140],"that":[36],"not":[38],"induced":[39],"any":[41],"non-trivially":[42],"partially":[43,87,142,181],"ordered":[44,88,143,182],"model":[45,89],"(order-incompleteness":[46],"problem).":[47],"In":[48],"terms":[49,179],"Alexandroff":[51,96,149,185,195],"topology":[52,55,97,150,186,196],"(the":[53],"strongest":[54],"whose":[56,141,184],"specialization":[57],"considered":[64],"model)":[65],"problem":[67],"order-incompleteness":[69,125],"can":[70],"be":[71],"also":[72],"characterized":[73],"as":[74],"follows:":[75],"T":[79,91],"order-incomplete":[81],"if,":[82,85],"only":[84],"every":[86,172],"partitioned":[93,146],"in":[98,151,178],"an":[99,121,152],"infinite":[100,153],"number":[101,154,190],"connected":[103,156,192],"components":[104,193],"(=":[105],"minimal":[106],"upper":[107],"lower":[109],"sets),":[110],"each":[111,158],"one":[112,115,159,163],"containing":[113,160],"exactly":[114],"element":[116],"model.":[119],"Towards":[120],"answer":[122],"problem,":[126],"we":[127],"give":[128],"topological":[130],"proof":[131],"following":[134],"result:":[135],"exists":[137],"components,":[157],"at":[161],"most":[162],"\u03bb-term":[164],"denotation.":[165],"This":[166],"result":[167],"implies":[168],"incompleteness":[170],"given":[177],"has":[187],"finite":[189],"(e.g.the":[194],"continuous,":[202],"stable":[203,206],"strongly":[205],"connected).":[209]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}