{"id":"https://openalex.org/W2010127229","doi":"https://doi.org/10.2178/jsl.7801160","title":"Universal sets for pointsets properly on the <i>n</i><sup>th</sup> level of the projective hierarchy","display_name":"Universal sets for pointsets properly on the <i>n</i><sup>th</sup> level of the projective hierarchy","publication_year":2013,"publication_date":"2013-01-23","ids":{"openalex":"https://openalex.org/W2010127229","doi":"https://doi.org/10.2178/jsl.7801160","mag":"2010127229"},"language":"en","primary_location":{"id":"doi:10.2178/jsl.7801160","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl.7801160","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":"The 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/A5044036779","display_name":"Greg Hjorth","orcid":null},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Greg Hjorth","raw_affiliation_strings":["Department of Mathematics & Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia, URL: www.math.ucla.edu/~greg, E-mail:","Department of Mathematics & Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia, URL: www.math.ucla.edu~greg, E-mail: leighh@unimelb.edu.au"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia, URL: www.math.ucla.edu/~greg, E-mail:","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Department of Mathematics & Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia, URL: www.math.ucla.edu~greg, E-mail: leighh@unimelb.edu.au","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004689292","display_name":"Leigh Humphries","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leigh Humphries","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5062397219","display_name":"Arnold W. Miller","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arnold W. Miller","raw_affiliation_strings":["University of Wisconsin-Madison, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388, USA, E-mail:","University of Wisconsin-Madison, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388, USA, E-mail: miller@math.wisc.edu URL: http/www.math.wisc.edu~miller"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388, USA, E-mail:","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin-Madison, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388, USA, E-mail: miller@math.wisc.edu URL: http/www.math.wisc.edu~miller","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0838569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"78","issue":"1","first_page":"237","last_page":"244"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9986000061035156,"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":0.9986000061035156,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/universal-set","display_name":"Universal set","score":0.6919447183609009},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6887491941452026},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6770956516265869},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.6580495834350586},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6101601719856262},{"id":"https://openalex.org/keywords/determinacy","display_name":"Determinacy","score":0.5517860054969788},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4331095218658447},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4309748411178589},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.429359495639801},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.41791489720344543},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19625318050384521},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09768083691596985},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0961751639842987},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.05127120018005371}],"concepts":[{"id":"https://openalex.org/C102565666","wikidata":"https://www.wikidata.org/wiki/Q1378301","display_name":"Universal set","level":3,"score":0.6919447183609009},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6887491941452026},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6770956516265869},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.6580495834350586},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6101601719856262},{"id":"https://openalex.org/C58468513","wikidata":"https://www.wikidata.org/wiki/Q1201165","display_name":"Determinacy","level":2,"score":0.5517860054969788},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4331095218658447},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4309748411178589},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.429359495639801},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.41791489720344543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19625318050384521},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09768083691596985},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0961751639842987},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.05127120018005371},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl.7801160","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl.7801160","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":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1358951111","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1358951111","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":[{"display_name":"Reduced inequalities","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1499443856","https://openalex.org/W1521767496","https://openalex.org/W1539382740","https://openalex.org/W1587975771","https://openalex.org/W1594319355","https://openalex.org/W1857413124","https://openalex.org/W1970364998","https://openalex.org/W1970531070","https://openalex.org/W1978413491","https://openalex.org/W1981403458","https://openalex.org/W4210359368","https://openalex.org/W4230295967","https://openalex.org/W4248784701","https://openalex.org/W4296119740"],"related_works":["https://openalex.org/W2088108327","https://openalex.org/W3037524176","https://openalex.org/W45652848","https://openalex.org/W1521335825","https://openalex.org/W2505787881","https://openalex.org/W1482555883","https://openalex.org/W4213060090","https://openalex.org/W4301421734","https://openalex.org/W4236657165","https://openalex.org/W579877627"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Axiom":[2],"of":[3,9],"Projective":[4],"Determinacy":[5],"implies":[6],"the":[7],"existence":[8],"a":[10,21,28],"universal":[11,22,29],"set":[12,30],"for":[13,31],"every":[14,32],"n":[15],"\u2265":[16],"1.":[17],"Assuming":[18],"there":[19,26],"exists":[20],"set.":[23],"In":[24],"ZFC":[25],"is":[27],"\u03b1":[33],".":[34]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
