{"id":"https://openalex.org/W4233762343","doi":"https://doi.org/10.1305/ndjfl/1168352667","title":"Level Compactness","display_name":"Level Compactness","publication_year":2006,"publication_date":"2006-10-01","ids":{"openalex":"https://openalex.org/W4233762343","doi":"https://doi.org/10.1305/ndjfl/1168352667"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1168352667","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1168352667","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/A5071141449","display_name":"Gillman Payette","orcid":"https://orcid.org/0000-0002-8499-1774"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gillman Payette","raw_affiliation_strings":["University of Notre Dame","Department of Philosophy Dalhousie University Halifax NS CANADA B3H 4P9"],"affiliations":[{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Department of Philosophy Dalhousie University Halifax NS CANADA B3H 4P9","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026304370","display_name":"Blaine d'Entremont","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Blaine d'Entremont","raw_affiliation_strings":["University of Notre Dame","Department of Philosophy Dalhousie University Halifax NS CANADA B3H 4P9"],"affiliations":[{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Department of Philosophy Dalhousie University Halifax NS CANADA B3H 4P9","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071141449"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.45317825,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"47","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9943000078201294,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9943000078201294,"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":0.9814000129699707,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9796000123023987,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.8782758712768555},{"id":"https://openalex.org/keywords/finitary","display_name":"Finitary","score":0.7792937755584717},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.66063392162323},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5757343173027039},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.5400295257568359},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5371646881103516},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5208533406257629},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4885428845882416},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.42138975858688354},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3753783702850342},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3443986773490906},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3200487792491913},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29829031229019165},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12478262186050415},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10729500651359558},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.08853965997695923}],"concepts":[{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.8782758712768555},{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.7792937755584717},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.66063392162323},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5757343173027039},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.5400295257568359},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5371646881103516},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5208533406257629},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4885428845882416},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.42138975858688354},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3753783702850342},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3443986773490906},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3200487792491913},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29829031229019165},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12478262186050415},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10729500651359558},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.08853965997695923},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1168352667","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1168352667","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/1168352667","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1168352667","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":[{"score":0.5199999809265137,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2034313967","https://openalex.org/W2047923802","https://openalex.org/W4233046245","https://openalex.org/W4297918538"],"related_works":["https://openalex.org/W2976590292","https://openalex.org/W4288102793","https://openalex.org/W4206837156","https://openalex.org/W2975654559","https://openalex.org/W2085314983","https://openalex.org/W2017288906","https://openalex.org/W3110583286","https://openalex.org/W4287587103","https://openalex.org/W2050219405","https://openalex.org/W2150101840"],"abstract_inverted_index":{"The":[0],"concept":[1,87],"of":[2,8,20,29,31,50,61,85,88,94,120,134,139],"compactness":[3,64,102],"is":[4,12,122],"a":[5,17,48,109,115],"necessary":[6],"condition":[7],"any":[9],"system":[10,128],"that":[11,37],"going":[13],"to":[14,27,45,90,107],"call":[15],"itself":[16],"finitary":[18],"method":[19],"proof.":[21],"However,":[22],"it":[23,39],"can":[24,40],"also":[25,81],"apply":[26,98],"predicates":[28],"sets":[30],"formulas":[32],"in":[33,36,43,72,104],"general":[34],"and":[35,63,66,77,114,136,141],"manner":[38],"be":[41],"used":[42],"relation":[44],"level":[46,89,101],"functions,":[47],"flavor":[49,111],"measure":[51,62],"functions.":[52],"In":[53],"what":[54],"follows":[55],"we":[56],"will":[57,80],"tie":[58],"these":[59,121],"concepts":[60,69],"together":[65],"expand":[67],"some":[68,83],"which":[70,130],"appear":[71],"d'Entremont's":[73],"master's":[74],"thesis,":[75],"\"Inference":[76],"Level.\"":[78],"We":[79,97],"provide":[82],"applications":[84],"the":[86,91,99],"\"preservationist\"":[92],"program":[93],"paraconsistent":[95],"logic.":[96],"finite":[100],"theorem":[103],"this":[105],"paper":[106],"get":[108],"Lindenbaum":[110],"extension":[112],"lemma":[113],"maximal":[116],"\"forcibility\"":[117],"theorem.":[118],"Each":[119],"based":[123],"on":[124],"an":[125],"abstract":[126],"deductive":[127],"X":[129],"satisfies":[131],"minimal":[132],"conditions":[133],"inference":[135],"has":[137],"generalizations":[138],"'and'":[140],"'not'":[142],"as":[143],"logical":[144],"words.":[145]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-05-12T00:00:00"}
