{"id":"https://openalex.org/W2060372513","doi":"https://doi.org/10.1305/ndjfl/1054837938","title":"Forcing Complexity: Minimum Sizes of Forcing Conditions","display_name":"Forcing Complexity: Minimum Sizes of Forcing Conditions","publication_year":2001,"publication_date":"2001-04-01","ids":{"openalex":"https://openalex.org/W2060372513","doi":"https://doi.org/10.1305/ndjfl/1054837938","mag":"2060372513"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1054837938","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1054837938","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-42/issue-2/Forcing-Complexity-Minimum-Sizes-of-Forcing-Conditions/10.1305/ndjfl/1054837938.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-42/issue-2/Forcing-Complexity-Minimum-Sizes-of-Forcing-Conditions/10.1305/ndjfl/1054837938.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040784460","display_name":"Toshio Suzuki","orcid":"https://orcid.org/0000-0002-7237-2650"},"institutions":[{"id":"https://openalex.org/I15807432","display_name":"Osaka Prefecture University","ror":"https://ror.org/02cf1je33","country_code":"JP","type":"education","lineage":["https://openalex.org/I15807432"]},{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["JP","US"],"is_corresponding":true,"raw_author_name":"Toshio Suzuki","raw_affiliation_strings":["Osaka Prefecture University Sakai Osaka 599-8531 JAPAN","University of Notre Dame Department of Mathematics and Information Sciences","Osaka  prefecture University"],"affiliations":[{"raw_affiliation_string":"Osaka Prefecture University Sakai Osaka 599-8531 JAPAN","institution_ids":["https://openalex.org/I15807432"]},{"raw_affiliation_string":"University of Notre Dame Department of Mathematics and Information Sciences","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Osaka  prefecture University","institution_ids":["https://openalex.org/I15807432"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040784460"],"corresponding_institution_ids":["https://openalex.org/I107639228","https://openalex.org/I15807432"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.17366412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"42","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9980999827384949,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9970999956130981,"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/forcing","display_name":"Forcing (mathematics)","score":0.8648648262023926},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.7596938610076904},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.6348181962966919},{"id":"https://openalex.org/keywords/lebesgue-measure","display_name":"Lebesgue measure","score":0.5597077012062073},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5551314353942871},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5549816489219666},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.5276036858558655},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.46841564774513245},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3492923378944397},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34082064032554626},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08432385325431824},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07246464490890503},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0634346604347229},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05193537473678589}],"concepts":[{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.8648648262023926},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.7596938610076904},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6348181962966919},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.5597077012062073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5551314353942871},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5549816489219666},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.5276036858558655},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.46841564774513245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3492923378944397},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34082064032554626},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08432385325431824},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07246464490890503},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0634346604347229},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05193537473678589}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1305/ndjfl/1054837938","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1054837938","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-42/issue-2/Forcing-Complexity-Minimum-Sizes-of-Forcing-Conditions/10.1305/ndjfl/1054837938.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1054837938","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1054837938","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.545.7695","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.545.7695","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ac.auone-net.jp/~bellp/toshio_suzuki_ndjfl42_2001.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1054837938","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1054837938","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-42/issue-2/Forcing-Complexity-Minimum-Sizes-of-Forcing-Conditions/10.1305/ndjfl/1054837938.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2060372513.pdf","grobid_xml":"https://content.openalex.org/works/W2060372513.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1982156324","https://openalex.org/W2058052847","https://openalex.org/W2062767125","https://openalex.org/W2133854625","https://openalex.org/W2170377962","https://openalex.org/W4244516892","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2074721578","https://openalex.org/W928772053","https://openalex.org/W3008743878","https://openalex.org/W2032212755","https://openalex.org/W2917668491","https://openalex.org/W4287864225","https://openalex.org/W3184958942","https://openalex.org/W4244471727","https://openalex.org/W1567236373","https://openalex.org/W105766698"],"abstract_inverted_index":{"This":[0],"note":[1],"is":[2],"a":[3,18,23,34,43],"continuation":[4],"of":[5,10,17,28,31,45,51],"our":[6],"former":[7],"paper":[8],"''Complexity":[9],"the":[11,15,29,49],"r-query":[12],"tautologies":[13],"in":[14,55],"presence":[16],"generic":[19],"oracle.''":[20],"We":[21,40],"give":[22],"very":[24],"short":[25],"direct":[26],"proof":[27,44],"nonexistence":[30],"t-generic":[32],"oracles,":[33],"result":[35,47],"obtained":[36],"first":[37],"by":[38],"Dowd.":[39],"also":[41],"reconstitute":[42],"Dowd's":[46],"that":[48],"class":[50],"all":[52],"r-generic":[53],"oracles":[54],"his":[56],"sense":[57],"has":[58],"Lebesgue":[59],"measure":[60],"one.":[61]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}