{"id":"https://openalex.org/W2046506404","doi":"https://doi.org/10.1142/s0219061313500037","title":"PROOF THEORY OF WEAK COMPACTNESS","display_name":"PROOF THEORY OF WEAK COMPACTNESS","publication_year":2013,"publication_date":"2013-03-21","ids":{"openalex":"https://openalex.org/W2046506404","doi":"https://doi.org/10.1142/s0219061313500037","mag":"2046506404"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061313500037","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061313500037","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1111.0462","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"TOSHIYASU ARAI","orcid":null},"institutions":[{"id":"https://openalex.org/I159385669","display_name":"Chiba University","ror":"https://ror.org/01hjzeq58","country_code":"JP","type":"education","lineage":["https://openalex.org/I159385669"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"TOSHIYASU ARAI","raw_affiliation_strings":["Graduate School of Science, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba 263-8522, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Science, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba 263-8522, Japan","institution_ids":["https://openalex.org/I159385669"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I159385669"],"apc_list":null,"apc_paid":null,"fwci":1.2418,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7781339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"01","first_page":"1350003","last_page":"1350003"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.983299970626831,"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":0.983299970626831,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.00559999980032444,"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"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.002199999988079071,"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/compact-space","display_name":"Compact space","score":0.8026999831199646},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.635200023651123},{"id":"https://openalex.org/keywords/continuum-hypothesis","display_name":"Continuum hypothesis","score":0.44519999623298645},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43470001220703125},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.4230000078678131},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.37860000133514404}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8478999733924866},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.8026999831199646},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.635200023651123},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48919999599456787},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4503999948501587},{"id":"https://openalex.org/C96488702","wikidata":"https://www.wikidata.org/wiki/Q208416","display_name":"Continuum hypothesis","level":2,"score":0.44519999623298645},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43470001220703125},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.4230000078678131},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.37860000133514404},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3052999973297119},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C171636804","wikidata":"https://www.wikidata.org/wiki/Q1149458","display_name":"Compactness theorem","level":4,"score":0.29350000619888306},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.265500009059906},{"id":"https://openalex.org/C102565666","wikidata":"https://www.wikidata.org/wiki/Q1378301","display_name":"Universal set","level":3,"score":0.2628999948501587},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0219061313500037","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061313500037","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1111.0462","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1111.0462","pdf_url":"https://arxiv.org/pdf/1111.0462","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1111.0462","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1111.0462","pdf_url":"https://arxiv.org/pdf/1111.0462","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1486629280","https://openalex.org/W1576539916","https://openalex.org/W1963953353","https://openalex.org/W1985231476","https://openalex.org/W2003387354","https://openalex.org/W2033008594","https://openalex.org/W2122092051","https://openalex.org/W2122314349"],"related_works":[],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"the":[3,11],"existence":[4],"of":[5,21],"a":[6],"weakly":[7],"compact":[8],"cardinal":[9],"over":[10],"Zermelo\u2013Fraenkel's":[12],"set":[13],"theory":[14],"ZF":[15],"is":[16],"proof-theoretically":[17],"reducible":[18],"to":[19],"iterations":[20],"Mostowski":[22],"collapsings":[23],"and":[24],"Mahlo":[25],"operations.":[26]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-06-24T00:00:00"}
