{"id":"https://openalex.org/W1967041984","doi":"https://doi.org/10.1305/ndjfl/1093956971","title":"A theorem on maximal sets.","display_name":"A theorem on maximal sets.","publication_year":1961,"publication_date":"1961-01-01","ids":{"openalex":"https://openalex.org/W1967041984","doi":"https://doi.org/10.1305/ndjfl/1093956971","mag":"1967041984"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093956971","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093956971","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal 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/A5087230935","display_name":"Joseph S. Ullian","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Joseph S. Ullian","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5087230935"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7051,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65754438,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.5200999975204468,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.5200999975204468,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.5038999915122986,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12508","display_name":"Functional Equations Stability Results","score":0.4406999945640564,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5977381467819214},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39831456542015076},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3365477919578552},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.07671889662742615}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5977381467819214},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39831456542015076},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3365477919578552},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07671889662742615},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093956971","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093956971","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1093956971","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093956971","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":2,"referenced_works":["https://openalex.org/W2905135108","https://openalex.org/W2913148016"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"We":[0],"presuppose":[1],"familiarity":[2],"with":[3,14],"[2].Let":[4],"21":[5,24,33,56,208],"be":[6,197],"the":[7],"class":[8],"of":[9,28,40,60,67,175,198],"recursively":[10],"enumerable":[11],"(r.e.)":[12],"sets":[13,42],"infinite":[15,111],"complements.A":[16],"r.e.set":[17,81],"M":[18,22,29],"is":[19,31,43,52,72,88,104,110,122,128,139,142,149,159,168],"maximal":[20,41,48,74,211],"if":[21],"\u20ac":[23,191],"and":[25,157],"every":[26,47,57,80,205],"r.e.superset":[27],"which":[30,61],"in":[32,45,55,113,200,207],"differs":[34],"only":[35],"finitely":[36,65],"from":[37,185],"M.":[38],"Existence":[39],"established":[44,143],"[l].Theorem-.For":[46],"set":[49,54,75,206],"W^,":[50],"there":[51,71],"a":[53,73,89,129,150,210],"recursive":[58,90,130,151],"permutation":[59,91,131],"lacks":[62],"at":[63],"most":[64],"much":[66],"WP":[68],"roof:":[69],"Otherwise,":[70],"W^":[76,103,121,124],"such":[77],"that":[78,145,162,187],"for":[79],"W":[82,84,95,98,117,189],"\u03c7)":[83],"e":[85,125,170,178],"2I^*(3":[86],"y)(\u03c6":[87,127],"&":[92,132],"x":[93],"y":[94,116,134],"z":[96,138],"~\u03a6y":[97],"\u03c7":[99,108,118,136,148,165,190],")":[100,109,119,166],"^":[101],"infinite).Since":[102],"maximal,":[105],"W^\u03c6":[106],"(W":[107,135,164],"just":[112],"case":[114],"\u03a6":[115],"~":[120],"finite.Thus":[123],"2ti^(:j":[126],"<\u00a3":[133],")-:W":[137],"finite).Now":[140],"it":[141,158],"in[3]":[144],"\\x\\":[146,188],"\u03c6":[147],"permutation}":[152],"=":[153,193],"S^2^\u20ac\u03aa\u03af":[154],"2":[155],",":[156,181],"easily":[160],"verified":[161],"{x\\\u03c6":[163],"-W^":[167],"finite}":[169],"\u03a3y":[171],"But":[172],"then":[173],"[xj^.h.s.":[174],"(1)":[176],"holds}":[177],"\u03a3":[179],"3":[180],"while":[182],"we":[183],"know":[184],"[2]":[186],"21}":[192],"This":[194],"result":[195],"may":[196],"help":[199],"determining":[201],"whether":[202],"or":[203],"not":[204],"has":[209],"superset.":[212]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
