{"id":"https://openalex.org/W2141464214","doi":"https://doi.org/10.2178/bsl/1107959499","title":"Proper Forcing, Cardinal Arithmetic, and Uncountable Linear Orders","display_name":"Proper Forcing, Cardinal Arithmetic, and Uncountable Linear Orders","publication_year":2005,"publication_date":"2005-03-01","ids":{"openalex":"https://openalex.org/W2141464214","doi":"https://doi.org/10.2178/bsl/1107959499","mag":"2141464214"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1107959499","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1107959499","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin 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/A5002552785","display_name":"Justin Tatch Moore","orcid":"https://orcid.org/0000-0003-2107-8547"},"institutions":[{"id":"https://openalex.org/I120156002","display_name":"Boise State University","ror":"https://ror.org/02e3zdp86","country_code":"US","type":"education","lineage":["https://openalex.org/I120156002"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Justin Tatch Moore","raw_affiliation_strings":["Department of Mathematics, Boise State University, Boise, Idaho 83725, USAE-mail:","Boise State University,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Boise State University, Boise, Idaho 83725, USAE-mail:","institution_ids":["https://openalex.org/I120156002"]},{"raw_affiliation_string":"Boise State University,","institution_ids":["https://openalex.org/I120156002"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002552785"],"corresponding_institution_ids":["https://openalex.org/I120156002"],"apc_list":null,"apc_paid":null,"fwci":0.4269,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6320679,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"1","first_page":"51","last_page":"60"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9983999729156494,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9952999949455261,"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/uncountable-set","display_name":"Uncountable set","score":0.904793381690979},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.8458935022354126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7840737104415894},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7140918970108032},{"id":"https://openalex.org/keywords/regular-cardinal","display_name":"Regular cardinal","score":0.5187790393829346},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.4921659827232361},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.48553726077079773},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4701889753341675},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46217647194862366},{"id":"https://openalex.org/keywords/continuum-hypothesis","display_name":"Continuum hypothesis","score":0.4420241713523865},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4322396218776703},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3637305498123169},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35653263330459595},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.22128000855445862},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13293111324310303},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.11045640707015991},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10685083270072937},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.08417057991027832},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07021847367286682},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.058752596378326416}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.904793381690979},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.8458935022354126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7840737104415894},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7140918970108032},{"id":"https://openalex.org/C89507440","wikidata":"https://www.wikidata.org/wiki/Q1193137","display_name":"Regular cardinal","level":2,"score":0.5187790393829346},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.4921659827232361},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.48553726077079773},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4701889753341675},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46217647194862366},{"id":"https://openalex.org/C96488702","wikidata":"https://www.wikidata.org/wiki/Q208416","display_name":"Continuum hypothesis","level":2,"score":0.4420241713523865},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4322396218776703},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3637305498123169},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35653263330459595},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.22128000855445862},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13293111324310303},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.11045640707015991},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10685083270072937},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.08417057991027832},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07021847367286682},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.058752596378326416},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/bsl/1107959499","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1107959499","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1107959499","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1107959499","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W81494948","https://openalex.org/W594310934","https://openalex.org/W952277824","https://openalex.org/W1582291305","https://openalex.org/W1591627679","https://openalex.org/W1594140616","https://openalex.org/W1601878490","https://openalex.org/W1981694349","https://openalex.org/W1995759544","https://openalex.org/W2025774568","https://openalex.org/W2032985500","https://openalex.org/W2061391432","https://openalex.org/W2063598253","https://openalex.org/W2070851509","https://openalex.org/W2079540958","https://openalex.org/W2087518766","https://openalex.org/W2090425123","https://openalex.org/W2111190351","https://openalex.org/W2117873821","https://openalex.org/W2121965785","https://openalex.org/W2134581608","https://openalex.org/W2135857723","https://openalex.org/W2152989620","https://openalex.org/W2319297044","https://openalex.org/W3021186728","https://openalex.org/W3190388120","https://openalex.org/W4210711493","https://openalex.org/W4210769709","https://openalex.org/W4234476515","https://openalex.org/W4250747102","https://openalex.org/W6645470815"],"related_works":["https://openalex.org/W4289676933","https://openalex.org/W2950296149","https://openalex.org/W2885719937","https://openalex.org/W4297981628","https://openalex.org/W2952331208","https://openalex.org/W4298219619","https://openalex.org/W3166038717","https://openalex.org/W2097355897","https://openalex.org/W2567038806","https://openalex.org/W2017366611"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"I":[4],"will":[5],"communicate":[6],"some":[7],"new":[8],"consequences":[9],"of":[10,28,51,78,81,106,122],"the":[11,16,43,49,79,92,97,120],"Proper":[12,18,44,93],"Forcing":[13,19,45,94],"Axiom.":[14],"First,":[15],"Bounded":[17],"Axiom":[20,46,95],"implies":[21,47,96],"that":[22,48],"there":[23],"is":[24,31,75,87],"a":[25,56],"well":[26],"ordering":[27],"\u211d":[29],"which":[30],"\u03a3":[32],"1":[33,66,84],"-definable":[34],"in":[35],"(":[36],"H(\u03c9":[37,123],"2":[38,124],"),":[39],"\u03f5":[40],").":[41],"Second,":[42],"class":[50],"uncountable":[52],"linear":[53],"orders":[54],"has":[55],"five":[57],"element":[58],"basis.":[59],"The":[60,108],"elements":[61],"are":[62,110],"X":[63,74],",":[64,67,68,70],"\u03c9":[65,83],"C":[69,71,86],"*":[72],"where":[73],"any":[76,88],"suborder":[77],"reals":[80],"size":[82],"and":[85],"Countryman":[89],"line.":[90],"Third,":[91],"Singular":[98],"Cardinals":[99],"Hypothesis":[100],"at":[101],"k":[102],"unless":[103],"stationary":[104],"subsets":[105],"reflect.":[107],"techniques":[109],"expected":[111],"to":[112,115],"be":[113],"applicable":[114],"other":[116],"open":[117],"problems":[118],"concerning":[119],"theory":[121],")":[125],".":[126]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
