{"id":"https://openalex.org/W2009263137","doi":"https://doi.org/10.1002/malq.19990450410","title":"Can You Add Power\u2010Sets to Martin\u2010Lof's Intuitionistic Set Theory?","display_name":"Can You Add Power\u2010Sets to Martin\u2010Lof's Intuitionistic Set Theory?","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2009263137","doi":"https://doi.org/10.1002/malq.19990450410","mag":"2009263137"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19990450410","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19990450410","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/A5053199287","display_name":"Maria Emilia Maietti","orcid":"https://orcid.org/0000-0002-9198-066X"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Maria Emilia Maietti","raw_affiliation_strings":["Dipartimento di Matematica Pura ed Applicata, Universita\u0301 di Padova, via G. Belzoni n. 7, I-35131 Padova, Italy","Dipartimento di Matematica Pura ed Applicata, Universit\u00e0 di Padova, via G. Belzoni n.7, I-35131 Padova, Italy#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica Pura ed Applicata, Universita\u0301 di Padova, via G. Belzoni n. 7, I-35131 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Dipartimento di Matematica Pura ed Applicata, Universit\u00e0 di Padova, via G. Belzoni n.7, I-35131 Padova, Italy#TAB#","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021932840","display_name":"Silvio Valentini","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Silvio Valentini","raw_affiliation_strings":["Dipartimento di Matematica Pura ed Applicata, Universita\u0301 di Padova, via G. Belzoni n. 7, I-35131 Padova, Italy","Dipartimento di Matematica Pura ed Applicata, Universit\u00e0 di Padova, via G. Belzoni n.7, I-35131 Padova, Italy#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica Pura ed Applicata, Universita\u0301 di Padova, via G. Belzoni n. 7, I-35131 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Dipartimento di Matematica Pura ed Applicata, Universit\u00e0 di Padova, via G. Belzoni n.7, I-35131 Padova, Italy#TAB#","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":2.0633,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.88096878,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"45","issue":"4","first_page":"521","last_page":"532"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9993000030517578,"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":0.9993000030517578,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9980000257492065,"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":0.9968000054359436,"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/extensionality","display_name":"Extensionality","score":0.9564602971076965},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.7779878377914429},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7445600032806396},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6626225113868713},{"id":"https://openalex.org/keywords/power-set","display_name":"Power set","score":0.6544555425643921},{"id":"https://openalex.org/keywords/proposition","display_name":"Proposition","score":0.6511430144309998},{"id":"https://openalex.org/keywords/universal-set","display_name":"Universal set","score":0.626160740852356},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5853115916252136},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.47098490595817566},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4264536201953888},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.40534508228302},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33702409267425537},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29061388969421387},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17297965288162231},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.1061277985572815},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.06191179156303406},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.059327930212020874},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.051941633224487305}],"concepts":[{"id":"https://openalex.org/C150355047","wikidata":"https://www.wikidata.org/wiki/Q965432","display_name":"Extensionality","level":2,"score":0.9564602971076965},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.7779878377914429},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7445600032806396},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6626225113868713},{"id":"https://openalex.org/C100643331","wikidata":"https://www.wikidata.org/wiki/Q205170","display_name":"Power set","level":3,"score":0.6544555425643921},{"id":"https://openalex.org/C2777152325","wikidata":"https://www.wikidata.org/wiki/Q108163","display_name":"Proposition","level":2,"score":0.6511430144309998},{"id":"https://openalex.org/C102565666","wikidata":"https://www.wikidata.org/wiki/Q1378301","display_name":"Universal set","level":3,"score":0.626160740852356},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5853115916252136},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.47098490595817566},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4264536201953888},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.40534508228302},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33702409267425537},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29061388969421387},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17297965288162231},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.1061277985572815},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.06191179156303406},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.059327930212020874},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.051941633224487305}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/malq.19990450410","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19990450410","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"},{"id":"pmh:oai:www.research.unipd.it:11577/2466079","is_oa":false,"landing_page_url":"http://hdl.handle.net/11577/2466079","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5099999904632568,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W4861723","https://openalex.org/W569543113","https://openalex.org/W1196275239","https://openalex.org/W1519680219","https://openalex.org/W1773829243","https://openalex.org/W2002359740","https://openalex.org/W2033165246","https://openalex.org/W2078334802","https://openalex.org/W2094931291","https://openalex.org/W2124729849","https://openalex.org/W2137702965","https://openalex.org/W2148713425","https://openalex.org/W2324455841","https://openalex.org/W2742270218","https://openalex.org/W2756921402","https://openalex.org/W3083054731"],"related_works":["https://openalex.org/W4388295869","https://openalex.org/W2098788035","https://openalex.org/W2009263137","https://openalex.org/W4237127835","https://openalex.org/W2106735727","https://openalex.org/W2152801202","https://openalex.org/W4388260123","https://openalex.org/W1446478209","https://openalex.org/W227442115","https://openalex.org/W4244929623"],"abstract_inverted_index":{"Abstract":[0],"In":[1,62],"this":[2,68],"paper":[3],"we":[4,64],"analyze":[5],"an":[6,57],"extension":[7,58,69],"of":[8,16,25,33,45],"Martin\u2010L\u00f6f":[9],"s":[10],"intensional":[11],"set":[12,18,35],"theory":[13],"by":[14],"means":[15],"a":[17],"contructor":[19],"P":[20,26],"such":[21,56],"that":[22,55,67,72],"the":[23,31,34,48],"elements":[24],"(":[27],"S":[28],")":[29,79],"are":[30],"subsets":[32],"S.":[36],"Since":[37],"it":[38,52],"seems":[39],"natural":[40],"to":[41],"require":[42],"some":[43],"kind":[44],"extensionality":[46],"on":[47],"equality":[49],"among":[50],"subsets,":[51],"turns":[53],"out":[54],"cannot":[59],"be":[60],"constructive.":[61],"fact":[63],"will":[65],"prove":[66],"is":[70,73],"classic,":[71],"\u201c(":[74],"A":[75,78],"V":[76],"\u231d":[77],"true":[80],"holds":[81],"for":[82],"any":[83],"proposition":[84],"A.":[85]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
