{"id":"https://openalex.org/W2009675710","doi":"https://doi.org/10.2307/2273546","title":"Set theory with a filter quantifier","display_name":"Set theory with a filter quantifier","publication_year":1983,"publication_date":"1983-06-01","ids":{"openalex":"https://openalex.org/W2009675710","doi":"https://doi.org/10.2307/2273546","mag":"2009675710"},"language":"en","primary_location":{"id":"doi:10.2307/2273546","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273546","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic 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/A5004178046","display_name":"Matt Kaufmann","orcid":"https://orcid.org/0009-0004-5667-4888"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matt Kaufmann","raw_affiliation_strings":["Purdue University, West Lafayette, Indiana 47907"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purdue University, West Lafayette, Indiana 47907","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004178046"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":1.3824,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.77914907,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"48","issue":"2","first_page":"263","last_page":"287"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9997000098228455,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9868000149726868,"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.9854999780654907,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7863106727600098},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.5810054540634155},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5483813285827637},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5437160730361938},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.4924691617488861},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4888402819633484},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.47320932149887085},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.4719970226287842},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.45393550395965576},{"id":"https://openalex.org/keywords/continuum-hypothesis","display_name":"Continuum hypothesis","score":0.43355658650398254},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.37129780650138855},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10111111402511597}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7863106727600098},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.5810054540634155},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5483813285827637},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5437160730361938},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.4924691617488861},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4888402819633484},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.47320932149887085},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.4719970226287842},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.45393550395965576},{"id":"https://openalex.org/C96488702","wikidata":"https://www.wikidata.org/wiki/Q208416","display_name":"Continuum hypothesis","level":2,"score":0.43355658650398254},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.37129780650138855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10111111402511597},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273546","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273546","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183741245","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183741245","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W6007438","https://openalex.org/W170265681","https://openalex.org/W429429566","https://openalex.org/W986162294","https://openalex.org/W1506418919","https://openalex.org/W1898322248","https://openalex.org/W2005800778","https://openalex.org/W2011178105","https://openalex.org/W2027753458","https://openalex.org/W2042173679","https://openalex.org/W2044107340","https://openalex.org/W2068218054","https://openalex.org/W2091476429","https://openalex.org/W2095271848","https://openalex.org/W2285371954","https://openalex.org/W2554842236","https://openalex.org/W2799061192","https://openalex.org/W4210589687","https://openalex.org/W4243558221"],"related_works":["https://openalex.org/W4214737172","https://openalex.org/W3012938552","https://openalex.org/W2324712051","https://openalex.org/W4287825236","https://openalex.org/W1239946963","https://openalex.org/W71729059","https://openalex.org/W1524103539","https://openalex.org/W3216731410","https://openalex.org/W1973527399","https://openalex.org/W2798639752"],"abstract_inverted_index":{"The":[0,68],"incompleteness":[1],"of":[2,13,22,82,120,138,146,152,170,173,181,183,187,189,192,201,207],"ZF":[3,14,23,184],"set":[4,56,126],"theory":[5,57,108,127],"leads":[6],"one":[7,17,39],"to":[8,26,33,148,159,166,185],"look":[9,53],"for":[10,71,106],"natural":[11],"extensions":[12],"in":[15,80,100,135,176,196,209],"which":[16,24,64,115,210],"can":[18,40],"prove":[19,160,167],"statements":[20],"independent":[21],"appear":[25],"be":[27],"\u201ctrue\u201d.":[28],"One":[29],"approach":[30],"has":[31],"been":[32],"add":[34],"large":[35],"cardinal":[36,90],"axioms.":[37],"Or,":[38],"investigate":[41,125],"second-order":[42],"expansions":[43],"like":[44],"Kelley-Morse":[45],"class":[46],"theory,":[47],"KM.":[48],"In":[49,122,140],"this":[50],"paper":[51],"we":[52,76,92,124,142,178],"at":[54],"a":[55,88,112,117,129,136,150,199],"ZF(aa),":[58],"with":[59,128,198],"an":[60,202],"added":[61],"quantifier":[62,212],"aa":[63,213],"ranges":[65],"over":[66],"ordinals.":[67],"\u201caa\u201d":[69],"stands":[70],"\u201calmost":[72],"all\u201d,":[73],"and":[74,110,132,191],"although":[75],"will":[77,93],"consider":[78,94],"interpretations":[79,96],"terms":[81],"the":[83,104,107,144,168,211],"closed":[84],"unbounded":[85],"filter":[86],"on":[87],"regular":[89],"\u03ba,":[91],"other":[95],"also.":[97],"We":[98,155,194],"start":[99],"\u00a71":[101],"by":[102],"giving":[103],"axioms":[105],"ZF(aa)":[109,190,204,208],"presenting":[111],"completeness":[113],"theorem":[114],"gives":[116],"model-theoretic":[118],"definition":[119],"ZF(aa).":[121,139,174],"\u00a72":[123,147],"satisfaction":[130,153],"predicate":[131],"interpret":[133],"it":[134],"fragment":[137],"\u00a73":[141],"generalize":[143],"methods":[145],"obtain":[149],"hierarchy":[151],"predicates.":[154],"use":[156],"these":[157],"predicates":[158],"reflection":[161],"theorems,":[162],"as":[163,165],"well":[164],"consistency":[169],"certain":[171],"fragments":[172,188],"Next,":[175],"\u00a74":[177],"discuss":[179],"expandability":[180],"models":[182,186],"Kelley-Morse.":[193],"conclude":[195],"\u00a75":[197],"discussion":[200],"extension":[203],"+":[205],"DET":[206],"is":[214],"self-dual.":[215]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
