{"id":"https://openalex.org/W1985422639","doi":"https://doi.org/10.2168/lmcs-8(4:7)2012","title":"On Berry's conjectures about the stable order in PCF","display_name":"On Berry's conjectures about the stable order in PCF","publication_year":2012,"publication_date":"2012-10-12","ids":{"openalex":"https://openalex.org/W1985422639","doi":"https://doi.org/10.2168/lmcs-8(4:7)2012","mag":"1985422639"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-8(4:7)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(4:7)2012","pdf_url":"https://lmcs.episciences.org/925/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/925/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042123096","display_name":"Fritz M\u00fcller","orcid":null},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Fritz M\u00fcller","raw_affiliation_strings":["saarland university"],"affiliations":[{"raw_affiliation_string":"saarland university","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042123096"],"corresponding_institution_ids":["https://openalex.org/I91712215"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07738425,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"Volume 8, Issue 4","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9934999942779541,"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/T10142","display_name":"Formal Methods in Verification","score":0.944100022315979,"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/finitary","display_name":"Finitary","score":0.8959598541259766},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.8118749260902405},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6200811862945557},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6019982695579529},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5527007579803467},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.433554470539093},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4043266773223877},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3495503067970276},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3376135230064392}],"concepts":[{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.8959598541259766},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.8118749260902405},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6200811862945557},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6019982695579529},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5527007579803467},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.433554470539093},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4043266773223877},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3495503067970276},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3376135230064392},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2168/lmcs-8(4:7)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(4:7)2012","pdf_url":"https://lmcs.episciences.org/925/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1108.0556","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1108.0556","pdf_url":"https://arxiv.org/pdf/1108.0556","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:d6dc7389e9a04337964b130088ed1691","is_oa":true,"landing_page_url":"https://doaj.org/article/d6dc7389e9a04337964b130088ed1691","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 8, Issue 4 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-8(4:7)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(4:7)2012","pdf_url":"https://lmcs.episciences.org/925/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1985422639.pdf","grobid_xml":"https://content.openalex.org/works/W1985422639.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W72610527","https://openalex.org/W128738456","https://openalex.org/W159715351","https://openalex.org/W1531786782","https://openalex.org/W1543173511","https://openalex.org/W1847465957","https://openalex.org/W1851099975","https://openalex.org/W1965557765","https://openalex.org/W1985955425","https://openalex.org/W2007270285","https://openalex.org/W2010959827","https://openalex.org/W2024189573","https://openalex.org/W2039112578","https://openalex.org/W2054717986","https://openalex.org/W2054969282","https://openalex.org/W2063805449","https://openalex.org/W2091935350","https://openalex.org/W2095636721","https://openalex.org/W2141746484","https://openalex.org/W2154851516","https://openalex.org/W2156992159","https://openalex.org/W2163554063","https://openalex.org/W2171525267","https://openalex.org/W2359106268","https://openalex.org/W2913281688","https://openalex.org/W2963495026","https://openalex.org/W4213275635","https://openalex.org/W4246262482"],"related_works":["https://openalex.org/W2333621390","https://openalex.org/W3099212081","https://openalex.org/W3213392216","https://openalex.org/W3030465535","https://openalex.org/W2095282951","https://openalex.org/W2928935854","https://openalex.org/W4288376543","https://openalex.org/W2122650439","https://openalex.org/W2086979258","https://openalex.org/W1576906924"],"abstract_inverted_index":{"PCF":[0,87,158,202],"is":[1,10,80,107,141,186],"a":[2,11,49,65,68,106,120,223],"sequential":[3],"simply":[4],"typed":[5],"lambda":[6],"calculus":[7],"language.":[8],"There":[9,168],"unique":[12],"order-extensional":[13],"fully":[14,198],"abstract":[15,199],"cpo":[16],"model":[17,37,97],"of":[18,25,88,95,115,159,176,201,207],"PCF,":[19],"built":[20],"up":[21],"from":[22],"equivalence":[23],"classes":[24],"terms.":[26],"In":[27],"1979,":[28],"G\\'erard":[29],"Berry":[30],"defined":[31],"the":[32,41,44,53,77,96,99,112,116,133,146,177,192,196,204,217],"stable":[33,45,60,78,93,113,178],"order":[34,46,61,79,94,101,114,211],"in":[35,111,145,156,203],"this":[36,72,153],"and":[38,43,59,121,130,162],"proved":[39],"that":[40,76,139,183],"extensional":[42],"together":[47],"form":[48,62,127],"bicpo.":[50],"He":[51],"made":[52],"following":[54],"two":[55],"conjectures:":[56],"1)":[57],"\"Extensional":[58],"not":[63,81],"only":[64],"bicpo,":[66],"but":[67],"bidomain.\"":[69],"We":[70,149],"refute":[71,164],"conjecture":[73,185],"by":[74],"showing":[75],"bounded":[82],"complete,":[83],"already":[84],"for":[85,118,188],"finitary":[86,157],"second-order":[89,160],"types.":[90],"2)":[91],"\"The":[92],"has":[98],"syntactic":[100,147,174],"as":[102],"its":[103],"image:":[104],"If":[105],"less":[108,142],"than":[109,143],"b":[110],"model,":[117],"finite":[119],"b,":[122,137],"then":[123],"there":[124],"are":[125],"normal":[126],"terms":[128],"A":[129,140],"B":[131,144],"with":[132,222],"semantics":[134,200],"a,":[135],"resp.":[136],"such":[138],"order.\"":[148],"give":[150],"counter-examples":[151],"to":[152,170,219],"conjecture,":[154],"again":[155],"types,":[161],"also":[163],"an":[165],"improved":[166],"conjecture:":[167],"seems":[169],"be":[171],"no":[172],"simple":[173],"characterization":[175],"order.":[179],"But":[180],"we":[181,194,215],"show":[182],"Berry's":[184],"true":[187],"unary":[189],"PCF.":[190],"For":[191],"preliminaries,":[193],"explain":[195],"basic":[197],"general":[205],"setting":[206],"(not-necessarily":[208],"complete)":[209],"partial":[210],"models":[212],"(f-models.)":[213],"And":[214],"restrict":[216],"syntax":[218],"\"game":[220],"terms\",":[221],"graphical":[224],"representation.":[225]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
