{"id":"https://openalex.org/W1978061618","doi":"https://doi.org/10.2307/2274659","title":"Hereditarily finite Finsler sets","display_name":"Hereditarily finite Finsler sets","publication_year":1990,"publication_date":"1990-06-01","ids":{"openalex":"https://openalex.org/W1978061618","doi":"https://doi.org/10.2307/2274659","mag":"1978061618"},"language":"en","primary_location":{"id":"doi:10.2307/2274659","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274659","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/A5025295787","display_name":"David Booth","orcid":"https://orcid.org/0000-0002-3032-3711"},"institutions":[{"id":"https://openalex.org/I94550122","display_name":"Waldorf College","ror":"https://ror.org/01qpf3c64","country_code":"US","type":"education","lineage":["https://openalex.org/I94550122"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David Booth","raw_affiliation_strings":["Green Meadows Waldorf School, Spring Valley, New York 10977","Green Meadows Waldorf School"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Green Meadows Waldorf School, Spring Valley, New York 10977","institution_ids":["https://openalex.org/I94550122"]},{"raw_affiliation_string":"Green Meadows Waldorf School","institution_ids":["https://openalex.org/I94550122"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025295787"],"corresponding_institution_ids":["https://openalex.org/I94550122"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.24775402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"55","issue":"2","first_page":"700","last_page":"706"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13703","display_name":"Attention Economy in Education and Business","score":0.6531000137329102,"subfield":{"id":"https://openalex.org/subfields/1408","display_name":"Strategy and Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T13703","display_name":"Attention Economy in Education and Business","score":0.6531000137329102,"subfield":{"id":"https://openalex.org/subfields/1408","display_name":"Strategy and Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12788","display_name":"Space Science and Extraterrestrial Life","score":0.5715000033378601,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/mathematics","display_name":"Mathematics","score":0.83228600025177},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.7505120635032654},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.6562595367431641},{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.6418973207473755},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5442743897438049},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5162037014961243},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.5056591033935547},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4724861979484558},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42898499965667725},{"id":"https://openalex.org/keywords/infinite-set","display_name":"Infinite set","score":0.42081689834594727},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11775550246238708},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10149678587913513},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08127152919769287}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.83228600025177},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.7505120635032654},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.6562595367431641},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.6418973207473755},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5442743897438049},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5162037014961243},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.5056591033935547},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4724861979484558},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42898499965667725},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.42081689834594727},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11775550246238708},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10149678587913513},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08127152919769287},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274659","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274659","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/1183743326","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743326","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":3,"referenced_works":["https://openalex.org/W1561011284","https://openalex.org/W2163851465","https://openalex.org/W3006020860"],"related_works":["https://openalex.org/W2480446702","https://openalex.org/W3139954723","https://openalex.org/W4242301765","https://openalex.org/W3019662020","https://openalex.org/W4207036583","https://openalex.org/W3033428001","https://openalex.org/W2488350907","https://openalex.org/W2790017930","https://openalex.org/W1986183533","https://openalex.org/W2081632957"],"abstract_inverted_index":{"Hereditarily":[0],"finite":[1,54,77,83,110,132,180],"sets":[2,4,55,66,84,111],"are":[3,6,10,17,25,67,128],"which":[5,64],"finite,":[7,11,18],"whose":[8,15],"members":[9,13,16],"the":[12,50,99,106,160,179,206,220,237],"of":[14,42,52,81,102,108,159,200,223],"and":[19,219],"so":[20],"on.":[21],"In":[22,59,115],"ZF":[23,37],"there":[24,127,229],"but":[26],"countably":[27],"many":[28,130],"such":[29],"sets;":[30,163],"they":[31],"constitute":[32],"V":[33],"\u03c9":[34],".":[35],"Were":[36],"to":[38,147,177,236,244],"lose":[39],"its":[40,195],"axiom":[41],"regularity,":[43],"however,":[44],"one":[45,88,241],"could":[46,85,112],"not":[47,97,187],"guarantee":[48],"that":[49,95,126,167],"number":[51,80,107],"hereditarily":[53,76,82,109,131],"would":[56,73],"remain":[57,113],"countable.":[58],"Mostowski":[60],"set":[61,117,184,225,247],"theory,":[62,118,248],"in":[63,71,92,139,173,245],"atomic":[65],"permissible,":[68],"each":[69],"atom,":[70],"isolation,":[72],"form":[74],"a":[75,93,188,198,231],"collection.":[78],"The":[79,134],"be":[86],"anything":[87],"should":[89],"choose.":[90],"Even":[91],"world":[94],"did":[96],"permit":[98],"free":[100],"adjunction":[101],"arbitrary,":[103],"meaningless":[104],"atoms,":[105],"large.":[114],"Finsler":[116,162,181,183],"it":[119,164],"is":[120,137,155,165,186,230,242],"shown":[121],"as":[122],"Theorem":[123],"22,":[124],"below,":[125],"uncountably":[129],"sets.":[133,182,211],"reader":[135],"who":[136],"interested":[138],"this":[140,168],"paradoxical":[141],"sounding":[142],"fact":[143],"can":[144,213],"turn":[145],"directly":[146],"\u00a74":[148],"after":[149],"grasping":[150],"these":[151],"introductory":[152],"concepts.":[153],"\u00a73":[154],"an":[156],"exhaustive":[157],"list":[158,169],"smallest":[161],"hoped":[166],"will":[170],"prove":[171],"useful":[172],"checking":[174],"future":[175],"attempts":[176],"classify":[178],"theory":[185,226],"firmly":[189],"axiomatized":[190],"theory.":[191],"It":[192,204],"is,":[193],"at":[194],"present":[196],"stage,":[197],"family":[199],"theories":[201],"undergoing":[202],"evolution.":[203],"permits":[205],"usual":[207,221],"mathematical":[208],"operations":[209],"with":[210],"One":[212],"employ":[214],"ordinal":[215],"numbers,":[216,218],"cardinal":[217],"methods":[222],"Cantorian":[224],"freely.":[227],"But":[228],"somewhat":[232],"different":[233],"interpretation":[234],"attached":[235],"concept":[238],"\u201cset\u201d":[239],"than":[240],"used":[243],"Zermelo-Fraenkel":[246],"ZF.":[249]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}