{"id":"https://openalex.org/W2111771095","doi":"https://doi.org/10.2178/bsl/1182353918","title":"Zermelo's Cantorian Theory of Systems of Infinitely Long Propositions","display_name":"Zermelo's Cantorian Theory of Systems of Infinitely Long Propositions","publication_year":2002,"publication_date":"2002-12-01","ids":{"openalex":"https://openalex.org/W2111771095","doi":"https://doi.org/10.2178/bsl/1182353918","mag":"2111771095"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1182353918","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1182353918","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/A5024737198","display_name":"Rob Taylor","orcid":"https://orcid.org/0000-0002-0983-7523"},"institutions":[{"id":"https://openalex.org/I4401726811","display_name":"Hartford Financial Services (United States)","ror":"https://ror.org/00mwq1g96","country_code":null,"type":"company","lineage":["https://openalex.org/I4401726811"]},{"id":"https://openalex.org/I56722557","display_name":"Trinity College","ror":"https://ror.org/03j3dbz94","country_code":"US","type":"education","lineage":["https://openalex.org/I56722557"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"R. Gregory Taylor","raw_affiliation_strings":["Trinity College, Hartford, CT 06106, USA, E-mail:","Trinity College"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Trinity College, Hartford, CT 06106, USA, E-mail:","institution_ids":["https://openalex.org/I56722557","https://openalex.org/I4401726811"]},{"raw_affiliation_string":"Trinity College","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024737198"],"corresponding_institution_ids":["https://openalex.org/I4401726811","https://openalex.org/I56722557"],"apc_list":null,"apc_paid":null,"fwci":0.7,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.69940672,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"8","issue":"4","first_page":"478","last_page":"515"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9921000003814697,"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":0.9921000003814697,"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":0.9884999990463257,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9602000117301941,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.890642523765564},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.7032022476196289},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6626389026641846},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.574178159236908},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.5704736709594727},{"id":"https://openalex.org/keywords/foundations-of-mathematics","display_name":"Foundations of mathematics","score":0.5558901429176331},{"id":"https://openalex.org/keywords/continuum-hypothesis","display_name":"Continuum hypothesis","score":0.5257278680801392},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.4972818195819855},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4881454408168793},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4513423442840576},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.4328559637069702},{"id":"https://openalex.org/keywords/g\u00f6dels-incompleteness-theorems","display_name":"G\u00f6del's incompleteness theorems","score":0.42510128021240234},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39254626631736755},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.39088380336761475},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3628702163696289},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3181915283203125},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.3145240843296051},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22740766406059265},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.15537774562835693},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12432372570037842},{"id":"https://openalex.org/keywords/g\u00f6del","display_name":"G\u00f6del","score":0.12061578035354614},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1050989031791687},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"Mathematics education","score":0.10002315044403076},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06155121326446533}],"concepts":[{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.890642523765564},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.7032022476196289},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6626389026641846},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.574178159236908},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.5704736709594727},{"id":"https://openalex.org/C183140480","wikidata":"https://www.wikidata.org/wiki/Q833585","display_name":"Foundations of mathematics","level":2,"score":0.5558901429176331},{"id":"https://openalex.org/C96488702","wikidata":"https://www.wikidata.org/wiki/Q208416","display_name":"Continuum hypothesis","level":2,"score":0.5257278680801392},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.4972818195819855},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4881454408168793},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4513423442840576},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.4328559637069702},{"id":"https://openalex.org/C180937797","wikidata":"https://www.wikidata.org/wiki/Q200787","display_name":"G\u00f6del's incompleteness theorems","level":3,"score":0.42510128021240234},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39254626631736755},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.39088380336761475},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3628702163696289},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3181915283203125},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.3145240843296051},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22740766406059265},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.15537774562835693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12432372570037842},{"id":"https://openalex.org/C2781302003","wikidata":"https://www.wikidata.org/wiki/Q3294091","display_name":"G\u00f6del","level":2,"score":0.12061578035354614},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1050989031791687},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.10002315044403076},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06155121326446533},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/bsl/1182353918","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1182353918","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/1182353918","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1182353918","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W794185885","https://openalex.org/W930256190","https://openalex.org/W943508897","https://openalex.org/W1540938302","https://openalex.org/W1607953571","https://openalex.org/W1965025401","https://openalex.org/W1977324591","https://openalex.org/W1985132925","https://openalex.org/W1989367560","https://openalex.org/W2011043790","https://openalex.org/W2026045585","https://openalex.org/W2029079161","https://openalex.org/W2063482927","https://openalex.org/W2063858946","https://openalex.org/W2067919976","https://openalex.org/W2072395631","https://openalex.org/W2073865413","https://openalex.org/W2097407030","https://openalex.org/W2114804254","https://openalex.org/W2485880037","https://openalex.org/W2496901757","https://openalex.org/W2588753921","https://openalex.org/W2998385477","https://openalex.org/W3022919901","https://openalex.org/W3152741257","https://openalex.org/W3179506523","https://openalex.org/W4232453619","https://openalex.org/W4238965074","https://openalex.org/W4240802416","https://openalex.org/W4256195314","https://openalex.org/W4256369010","https://openalex.org/W6666523140"],"related_works":["https://openalex.org/W1572152362","https://openalex.org/W9892475","https://openalex.org/W126781605","https://openalex.org/W2765595756","https://openalex.org/W936105296","https://openalex.org/W2130992033","https://openalex.org/W2188217989","https://openalex.org/W258515149","https://openalex.org/W2111771095","https://openalex.org/W4254723759"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"papers":[2],"published":[3],"between":[4,61],"1930":[5],"and":[6,33,35,63,71,84,98],"1935,":[7],"Zermelo":[8,86],"outlines":[9],"a":[10,29,58,67],"foundational":[11],"program,":[12],"with":[13],"infinitary":[14],"logic":[15],"at":[16],"its":[17],"heart,":[18],"that":[19,38,57],"is":[20,88,105],"intended":[21],"to":[22,76],"(1)":[23],"secure":[24],"axiomatic":[25],"set":[26],"theory":[27,45],"as":[28],"foundation":[30],"for":[31],"arithmetic":[32],"analysis":[34],"(2)":[36],"show":[37],"all":[39],"mathematical":[40],"propositions":[41,51],"are":[42,74],"decidable.":[43],"Zermelo's":[44],"of":[46,48,82,92,95,101],"systems":[47],"infinitely":[49],"long":[50],"may":[52],"be":[53],"termed":[54],"\u201cCantorian\u201d":[55],"in":[56],"logical":[59],"distinction":[60],"open":[62],"closed":[64],"domains":[65],"plays":[66],"signal":[68],"role.":[69],"Well-foundedness":[70],"strong":[72],"inaccessibility":[73],"used":[75],"systematically":[77],"integrate":[78],"highly":[79],"transfinite":[80],"concepts":[81],"demonstrability":[83],"existence.":[85],"incompleteness":[87],"then":[89],"the":[90,93,99],"analogue":[91],"Problem":[94],"Proper":[96],"Classes,":[97],"resolution":[100],"these":[102],"two":[103],"anomalies":[104],"similarly":[106],"analogous.":[107]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}