{"id":"https://openalex.org/W1495351994","doi":"https://doi.org/10.2178/jsl/1190150154","title":"Bounded Martin's Maximum, weak Erd\u04e7s cardinals, and <i>\u03c8</i><sub><i>Ac</i></sub>","display_name":"Bounded Martin's Maximum, weak Erd\u04e7s cardinals, and <i>\u03c8</i><sub><i>Ac</i></sub>","publication_year":2002,"publication_date":"2002-09-01","ids":{"openalex":"https://openalex.org/W1495351994","doi":"https://doi.org/10.2178/jsl/1190150154","mag":"1495351994"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1190150154","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150154","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":"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/A5017293866","display_name":"David Asper\u00f3","orcid":"https://orcid.org/0000-0002-7972-2860"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"David Asper\u00f3","raw_affiliation_strings":["Institut F\u00fcr Formale Logik, Universit\u00e4t Wien, W\u00e4hringerstr. 25, A-1090 Wien, Austria, E-mail:","UNIVERSITAT WIEN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut F\u00fcr Formale Logik, Universit\u00e4t Wien, W\u00e4hringerstr. 25, A-1090 Wien, Austria, E-mail:","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"UNIVERSITAT WIEN","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051447400","display_name":"Philip Welch","orcid":"https://orcid.org/0000-0001-8350-1430"},"institutions":[{"id":"https://openalex.org/I75971999","display_name":"Centre for Science and Environment","ror":"https://ror.org/053e12g40","country_code":"IN","type":"nonprofit","lineage":["https://openalex.org/I75971999"]},{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT","IN"],"is_corresponding":false,"raw_author_name":"Philip D. Welch","raw_affiliation_strings":["Institut F\u00fcr Formale Logik, Universit\u00e4t Wien, W\u00e4hringerstr. 25, A-1090 Wien, Austria, E-mail:","Centre for Science and Philosophy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut F\u00fcr Formale Logik, Universit\u00e4t Wien, W\u00e4hringerstr. 25, A-1090 Wien, Austria, E-mail:","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Centre for Science and Philosophy","institution_ids":["https://openalex.org/I75971999"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017293866"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":null,"apc_paid":null,"fwci":0.9718,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.69387498,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"67","issue":"3","first_page":"1141","last_page":"1152"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":1.0,"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":1.0,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9973000288009644,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9965999722480774,"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/bounded-function","display_name":"Bounded function","score":0.8712018728256226},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6963040828704834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6303502917289734},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5822969079017639},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.5464257001876831},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5357825756072998},{"id":"https://openalex.org/keywords/bounded-deformation","display_name":"Bounded deformation","score":0.4509503245353699},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4407029151916504},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4002637267112732},{"id":"https://openalex.org/keywords/bounded-operator","display_name":"Bounded operator","score":0.2572818696498871},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11348098516464233}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.8712018728256226},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6963040828704834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6303502917289734},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5822969079017639},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.5464257001876831},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5357825756072998},{"id":"https://openalex.org/C92928283","wikidata":"https://www.wikidata.org/wiki/Q4949981","display_name":"Bounded deformation","level":4,"score":0.4509503245353699},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4407029151916504},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4002637267112732},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.2572818696498871},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11348098516464233},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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":3,"locations":[{"id":"doi:10.2178/jsl/1190150154","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150154","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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1190150154","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1190150154","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:ueaeprints.uea.ac.uk:44046","is_oa":false,"landing_page_url":"https://ueaeprints.uea.ac.uk/id/eprint/44046/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400384","display_name":"UEA Digital Repository (University of East Anglia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1118541","host_organization_name":"University of East Anglia","host_organization_lineage":["https://openalex.org/I1118541"],"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":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1963763200","https://openalex.org/W1989534953","https://openalex.org/W2020542356","https://openalex.org/W2072992387","https://openalex.org/W2090425123","https://openalex.org/W2111190351","https://openalex.org/W2117873821","https://openalex.org/W2121965785","https://openalex.org/W2319297044","https://openalex.org/W2324217417","https://openalex.org/W2949854457"],"related_works":["https://openalex.org/W2992829260","https://openalex.org/W4287998863","https://openalex.org/W2927651154","https://openalex.org/W3209780287","https://openalex.org/W4289753045","https://openalex.org/W2389758888","https://openalex.org/W2044249119","https://openalex.org/W2963327521","https://openalex.org/W2372392521","https://openalex.org/W2356614471"],"abstract_inverted_index":{"Abstract":[0],"We":[1,45],"prove":[2,47],"that":[3,36,48,52],"a":[4,69,76],"form":[5],"of":[6,78],"the":[7,22,79],"Erd\u04e7s":[8],"property":[9],"(consistent":[10],"with":[11,31],"V":[12],"=":[13],"L":[14],"[H\u03c9":[15],"2":[16],"]":[17],"and":[18,42,71],"strictly":[19],"weaker":[20],"than":[21],"Weak":[23],"Chang's":[24],"Conjecture":[25],"at":[26],"\u03c9":[27,57,60],"1":[28,58,61],"),":[29],"together":[30],"Bounded":[32,80,86],"Martin's":[33,87],"Maximum":[34,88],"implies":[35,51],"Woodin's":[37],"principle":[38],"\u03c8":[39,49],"AC":[40,50],"holds,":[41],"therefore":[43],".":[44],"also":[46],"every":[53],"function":[54,67],"f":[55],":":[56],"\u2192":[59],"is":[62],"bounded":[63],"by":[64],"some":[65],"canonical":[66],"on":[68],"club":[70],"use":[72],"this":[73],"to":[74],"produce":[75],"model":[77],"Semiproper":[81],"Forcing":[82],"Axiom":[83],"in":[84],"which":[85],"fails.":[89]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-04-26T08:31:28.666265","created_date":"2016-06-24T00:00:00"}