{"id":"https://openalex.org/W2561153585","doi":"https://doi.org/10.1215/00294527-2017-0009","title":"Decidable Fragments of the Simple Theory of Types with Infinity and NF","display_name":"Decidable Fragments of the Simple Theory of Types with Infinity and NF","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2561153585","doi":"https://doi.org/10.1215/00294527-2017-0009","mag":"2561153585"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-2017-0009","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2017-0009","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-58/issue-3/Decidable-Fragments-of-the-Simple-Theory-of-Types-with-Infinity/10.1215/00294527-2017-0009.pdf","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-58/issue-3/Decidable-Fragments-of-the-Simple-Theory-of-Types-with-Infinity/10.1215/00294527-2017-0009.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Anuj Dawar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anuj Dawar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Thomas Forster","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas Forster","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Zachiri McKenzie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zachiri McKenzie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2274,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65443191,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"58","issue":"3","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":0.6324999928474426,"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":0.6324999928474426,"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.1290999948978424,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.060600001364946365,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/decidability","display_name":"Decidability","score":0.8526999950408936},{"id":"https://openalex.org/keywords/stratification","display_name":"Stratification (seeds)","score":0.717199981212616},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.7111999988555908},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.6732000112533569},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6251000165939331},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5393999814987183},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46320000290870667}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8526999950408936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7366999983787537},{"id":"https://openalex.org/C192943249","wikidata":"https://www.wikidata.org/wiki/Q1893382","display_name":"Stratification (seeds)","level":5,"score":0.717199981212616},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.7111999988555908},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.6732000112533569},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6251000165939331},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5393999814987183},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4212000072002411},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.3928000032901764},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.359499990940094},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35830000042915344},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.3549000024795532},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3174000084400177},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.2524999976158142}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1215/00294527-2017-0009","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2017-0009","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-58/issue-3/Decidable-Fragments-of-the-Simple-Theory-of-Types-with-Infinity/10.1215/00294527-2017-0009.pdf","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:arXiv.org:1406.4384","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1406.4384","pdf_url":"https://arxiv.org/pdf/1406.4384","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:CULeuclid:euclid.ndjfl/1492761612","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1492761612","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":{"id":"doi:10.1215/00294527-2017-0009","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2017-0009","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-58/issue-3/Decidable-Fragments-of-the-Simple-Theory-of-Types-with-Infinity/10.1215/00294527-2017-0009.pdf","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2470687288","display_name":null,"funder_award_id":"EP/H026835/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3348103018","display_name":null,"funder_award_id":"EP/H026835","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2561153585.pdf","grobid_xml":"https://content.openalex.org/works/W2561153585.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1979425288","https://openalex.org/W2091425612","https://openalex.org/W2319520949","https://openalex.org/W4388295869"],"related_works":[],"abstract_inverted_index":{"We":[0,20],"identify":[1],"complete":[2],"fragments":[3],"of":[4,8,31,38,50,66,85,92,113,135],"the":[5,29,39,45,48,51,61,64,67,83,93,114,130,136],"simple":[6],"theory":[7,33,87],"types":[9,49,65],"with":[10],"infinity":[11],"(TSTI)":[12],"and":[13,54,69,102,123],"Quine\u2019s":[14],"new":[15],"foundations":[16],"(NF)":[17],"set":[18,86],"theory.":[19],"show":[21],"that":[22,34,75,88,107,128],"TSTI":[23],"decides":[24,77],"every":[25,78],"sentence":[26,80],"\u03d5":[27,81,103,124],"in":[28,36,82,90],"language":[30,84],"type":[32],"is":[35,56,71,89,100,121],"one":[37,91],"following":[40,94],"forms:":[41,95],"(A)":[42],"\u03d5=\u2200x1r1\u22ef\u2200xkrk\u2203y1s1\u22ef\u2203ylsl\u03b8":[43],"where":[44,60,98,119],"superscripts":[46,62],"denote":[47,63],"variables,":[52],"s1>\u22ef>sl,":[53],"\u03b8":[55,70,99,120],"quantifier-free,":[57],"(B)":[58],"\u03d5=\u2200x1r1\u22ef\u2200xkrk\u2203y1s\u22ef\u2203yls\u03b8":[59],"variables":[68,115,137],"quantifier-free.":[72],"This":[73],"shows":[74],"NF":[76],"stratified":[79],"(A\u2032)":[96],"\u03d5=\u2200x1\u22ef\u2200xk\u2203y1\u22ef\u2203yl\u03b8":[97,118],"quantifier-free":[101,122],"admits":[104,125],"a":[105,126],"stratification":[106,127],"assigns":[108,129],"distinct":[109],"values":[110],"to":[111,133],"all":[112,134],"y1,\u2026,yl,":[116],"(B\u2032)":[117],"same":[131],"value":[132],"y1,\u2026,yl.":[138]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2017-01-06T00:00:00"}
