{"id":"https://openalex.org/W1977107423","doi":"https://doi.org/10.1002/malq.19920380110","title":"THE DECISION PROBLEM FOR RESTRICTED UNIVERSAL QUANTIFICATION IN SET THEORY AND THE AXIOM OF FOUNDATION","display_name":"THE DECISION PROBLEM FOR RESTRICTED UNIVERSAL QUANTIFICATION IN SET THEORY AND THE AXIOM OF FOUNDATION","publication_year":1992,"publication_date":"1992-01-01","ids":{"openalex":"https://openalex.org/W1977107423","doi":"https://doi.org/10.1002/malq.19920380110","mag":"1977107423"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19920380110","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19920380110","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5055139955","display_name":"Franco Parlamento","orcid":"https://orcid.org/0000-0003-1430-960X"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Franco Parlamento","raw_affiliation_strings":["Dipartimento di Matematica e Informatica Universita\u0300 di Udine Via Zanon 6 33100 Udine Italy","Dipartimento di Matematica e Informatica Universit\u00e0 di Udine Via Zanon 6 33100 Udine Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica Universita\u0300 di Udine Via Zanon 6 33100 Udine Italy","institution_ids":["https://openalex.org/I129043915"]},{"raw_affiliation_string":"Dipartimento di Matematica e Informatica Universit\u00e0 di Udine Via Zanon 6 33100 Udine Italy","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042115100","display_name":"Alberto Policriti","orcid":"https://orcid.org/0000-0001-8502-5896"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Policriti","raw_affiliation_strings":["Dipartimento di Matematica e Informatica Universita\u0300 di Udine Via Zanon 6 33100 Udine Italy","Dipartimento di Matematica e Informatica Universit\u00e0 di Udine Via Zanon 6 33100 Udine Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica Universita\u0300 di Udine Via Zanon 6 33100 Udine Italy","institution_ids":["https://openalex.org/I129043915"]},{"raw_affiliation_string":"Dipartimento di Matematica e Informatica Universit\u00e0 di Udine Via Zanon 6 33100 Udine Italy","institution_ids":["https://openalex.org/I129043915"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I129043915"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":1.4347,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.79833855,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"38","issue":"1","first_page":"143","last_page":"156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9943000078201294,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9943000078201294,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9581999778747559,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9401999711990356,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8293022513389587},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7149649858474731},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.7020590901374817},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.6554564237594604},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.6275686025619507},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6179490685462952},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.6130838394165039},{"id":"https://openalex.org/keywords/urelement","display_name":"Urelement","score":0.5537096261978149},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5163268446922302},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4921244978904724},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.49049991369247437},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.4827934503555298},{"id":"https://openalex.org/keywords/constructive-set-theory","display_name":"Constructive set theory","score":0.4652961492538452},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.43547922372817993},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.35827478766441345},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08629021048545837}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8293022513389587},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7149649858474731},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.7020590901374817},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.6554564237594604},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.6275686025619507},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6179490685462952},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.6130838394165039},{"id":"https://openalex.org/C78550038","wikidata":"https://www.wikidata.org/wiki/Q1896657","display_name":"Urelement","level":5,"score":0.5537096261978149},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5163268446922302},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4921244978904724},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.49049991369247437},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4827934503555298},{"id":"https://openalex.org/C556429856","wikidata":"https://www.wikidata.org/wiki/Q5164501","display_name":"Constructive set theory","level":5,"score":0.4652961492538452},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.43547922372817993},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.35827478766441345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08629021048545837},{"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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","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},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19920380110","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19920380110","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7799999713897705,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W27221543","https://openalex.org/W1543866088","https://openalex.org/W1561011284","https://openalex.org/W1977686940","https://openalex.org/W1994793938","https://openalex.org/W1996920632","https://openalex.org/W2005661612","https://openalex.org/W2026387431","https://openalex.org/W2068930233","https://openalex.org/W2087640143","https://openalex.org/W2101118111","https://openalex.org/W2572596860","https://openalex.org/W4255884887"],"related_works":["https://openalex.org/W2016661762","https://openalex.org/W1574825745","https://openalex.org/W2079743999","https://openalex.org/W2741238752","https://openalex.org/W1538212383","https://openalex.org/W2008703337","https://openalex.org/W2009439044","https://openalex.org/W3197691547","https://openalex.org/W2060433450","https://openalex.org/W1511476185"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"still":[2,137],"unsettled":[3],"decision":[4],"problem":[5,48,112,136,154,181,206],"for":[6,49,182,203,209],"the":[7,16,30,35,40,44,50,55,61,76,83,110,119,130,143,152,176,179,183,204,215],"restricted":[8,98,212],"purely":[9],"universal":[10],"formulae":[11,62],"((\u2200)":[12],"0":[13,57,188,217],"\u2010formulae)":[14],"of":[15,34,37,42,54,60,67,78,90,121,132,146,172,178,186,214],"first":[17],"order":[18],"set\u2010theoretic":[19],"language":[20],"based":[21],"over":[22,82,102],"=,":[23],"\u2208":[24],"is":[25,70,113,123,127,155,190,198],"discussed":[26],"in":[27,104,140],"relation":[28],"with":[29,106,160],"adoption":[31,145],"or":[32],"rejection":[33],"axiom":[36,41,120,149],"foundation.":[38],"Assuming":[39],"foundation,":[43],"related":[45,134],"finite":[46,85],"set\u2010satisfiability":[47,111,153,180,205],"very":[51,211],"significant":[52],"subclass":[53,213],"(\u2200)":[56],"\u2010formulae":[58,189],"consisting":[59],"involving":[63],"only":[64,101],"nested":[65],"variables":[66,96],"level":[68],"1":[69],"proved":[71],"to":[72,99,115,164,192,201],"be":[73,116,193],"semidecidable":[74],"on":[75],"ground":[77],"a":[79,133,170,195,210],"reflection":[80],"property":[81],"hereditarily":[84],"sets,":[86,103],"and":[87],"various":[88],"extensions":[89],"this":[91],"result":[92,196],"are":[93,97],"obtained.":[94],"When":[95],"range":[100],"universes":[105],"infinitely":[107],"many":[108],"urelements":[109],"shown":[114,191],"solvable":[117,157],"provided":[118],"foundation":[122],"assumed;":[124],"if":[125],"it":[126],"not,":[128],"then":[129],"decidability":[131],"derivability":[135],"holds.":[138],"That,":[139],"turn,":[141],"suggests":[142],"alternative":[144],"an":[147],"antifoundation":[148,174],"under":[150],"which":[151],"also":[156],"(of":[158],"course":[159],"different":[161],"answers).":[162],"Turning":[163],"set":[165],"theory":[166],"without":[167],"urelements,":[168],"assuming":[169],"form":[171],"Boffa's":[173],"axiom,":[175],"complement":[177],"full":[184],"class":[185],"\u0394":[187,216],"semidecidable;":[194],"that":[197],"known":[199],"not":[200],"hold,":[202],"itself,":[207],"even":[208],"\u2010formulae.":[218]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2025-10-10T00:00:00"}