{"id":"https://openalex.org/W2171124436","doi":"https://doi.org/10.2307/2273708","title":"The measure quantifier","display_name":"The measure quantifier","publication_year":1979,"publication_date":"1979-03-01","ids":{"openalex":"https://openalex.org/W2171124436","doi":"https://doi.org/10.2307/2273708","mag":"2171124436"},"language":"en","primary_location":{"id":"doi:10.2307/2273708","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273708","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/A5002485262","display_name":"Carl F. Morgenstern","orcid":null},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Carl F. Morgenstern","raw_affiliation_strings":["University of California, Santa Cruz, Ca 95064"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Santa Cruz, Ca 95064","institution_ids":["https://openalex.org/I185103710"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002485262"],"corresponding_institution_ids":["https://openalex.org/I185103710"],"apc_list":null,"apc_paid":null,"fwci":0.637,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.725242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"44","issue":"1","first_page":"103","last_page":"108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9934999942779541,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9873999953269958,"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/mathematics","display_name":"Mathematics","score":0.7696455717086792},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.68426913022995},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6783246397972107},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6764369010925293},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.5925774574279785},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5717855095863342},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5270773768424988},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.48034441471099854},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.4776783585548401},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.47058573365211487},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35413920879364014},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3469845652580261},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1308726668357849},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07962864637374878}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7696455717086792},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.68426913022995},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6783246397972107},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6764369010925293},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.5925774574279785},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5717855095863342},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5270773768424988},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48034441471099854},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.4776783585548401},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.47058573365211487},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35413920879364014},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3469845652580261},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1308726668357849},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07962864637374878},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273708","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273708","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/1183740349","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183740349","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":7,"referenced_works":["https://openalex.org/W649308871","https://openalex.org/W1574937548","https://openalex.org/W2005800778","https://openalex.org/W2026216307","https://openalex.org/W2066633462","https://openalex.org/W4210589687","https://openalex.org/W6601094266"],"related_works":["https://openalex.org/W2376029318","https://openalex.org/W2388301251","https://openalex.org/W3013941779","https://openalex.org/W1998659141","https://openalex.org/W3195376785","https://openalex.org/W2370435933","https://openalex.org/W2171296020","https://openalex.org/W2914340511","https://openalex.org/W3042258492","https://openalex.org/W4254309379"],"abstract_inverted_index":{"Originally":[0],"generalized":[1],"quantifiers":[2,158,175],"were":[3],"introduced":[4],"to":[5,69,139,169,183,212],"specify":[6],"that":[7,53,99],"a":[8,79,85,88,110,130,137,202,229],"given":[9],"formula":[10],"was":[11],"true":[12,58],"for":[13,191],"\u201cmany":[14],"x's\u201d":[15],"e.g.":[16],"\u22a8":[17,30],"Q":[18,112,159,176],"x":[19,21,25,32,55,62],"\u03c6(":[20],")":[22,56,75],"iff":[23],"card{":[24],"\u2208":[26,164,181],"\u2223":[27,28,29],"\u03c6[":[31],"]}":[33],"\u2265":[34],"\u2135":[35,38,206],"0":[36,207],",":[37,40,114],"1":[39],"or":[41],"some":[42],"fixed":[43],"cardinal":[44,204],"\u03ba.":[45],"In":[46],"this":[47],"paper":[48],"we":[49,125,143],"formalize":[50],"the":[51,92,100,118,127,140,145,149,156],"notion":[52],"\u03c6{":[54],"is":[57,65,78,84,121,189,201],"\u201cfor":[59,214],"almost":[60,215],"all":[61],"\u201d.":[63],"This":[64],"accomplished":[66],"by":[67,108,221],"referring":[68],"structures":[70],"=":[71],"(":[72,162,179],"\u2032,":[73],"\u03bc":[74,83,103,113,153,171,177],"where":[76,199],"\u2032":[77],"first-order":[80,106],"structure":[81],"and":[82,224],"measure":[86,119],"of":[87,94,129,133,148,151,193,195,231],"suitable":[89],"type":[90],"on":[91],"universe":[93],"\u2032.":[95],"We":[96],"will":[97,166],"prove":[98],"language":[101],"L":[102,152,170,185],"obtained":[104],"from":[105],"logic":[107],"adjoining":[109],"quantifier":[111],"which":[115,188],"ranges":[116],"over":[117],"\u03bc,":[120],"fully":[122],"compact":[123,190],"if":[124],"assume":[126],"existence":[128],"proper":[131],"class":[132],"measurable":[134,203],"cardinals.":[135],"As":[136],"corollary":[138],"compactness":[141],"theorem":[142],"obtain":[144],"recursive":[146],"enumerability":[147],"validities":[150],".":[154,208],"Finally,":[155],"Magidor-Malitz":[157],"k":[160],"n":[161,163],"\u03c9)":[165,182],"be":[167],"added":[168],"together":[172],"with":[173],"analogous":[174],"m":[178,180],"form":[184],"\u03ba\u03bc":[186],"<\u03c9,<\u03c9,":[187],"sets":[192],"sentences":[194],"cardinality":[196],"<":[197],"\u03ba,":[198],"\u03ba":[200],">":[205],"An":[209],"alternate":[210],"approach":[211],"formalizing":[213],"all\u201d":[216],"has":[217],"been":[218],"recently":[219],"developed":[220],"Barwise,":[222],"Kaufmann":[223],"Makkai":[225],"[1]":[226],"who":[227],"follow":[228],"suggestion":[230],"Shelah":[232],"[5].":[233]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}