{"id":"https://openalex.org/W4239786980","doi":"https://doi.org/10.2307/2271954","title":"Provable wellorderings of formal theories for transfinitely iterated inductive definitions","display_name":"Provable wellorderings of formal theories for transfinitely iterated inductive definitions","publication_year":1978,"publication_date":"1978-03-01","ids":{"openalex":"https://openalex.org/W4239786980","doi":"https://doi.org/10.2307/2271954"},"language":"en","primary_location":{"id":"doi:10.2307/2271954","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271954","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/A5058400297","display_name":"Wilfried Buchholz","orcid":null},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"W. Buchholz","raw_affiliation_strings":["Mathematisches Institut der Ludwig-Maximilians-Universit\u00e4t, M\u00fcnchen, Federal Republic of Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut der Ludwig-Maximilians-Universit\u00e4t, M\u00fcnchen, Federal Republic of Germany","institution_ids":["https://openalex.org/I8204097"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049894923","display_name":"Wolfram Pohlers","orcid":null},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"W. Pohlers","raw_affiliation_strings":["Mathematisches Institut der Ludwig-Maximilians-Universit\u00e4t, M\u00fcnchen, Federal Republic of Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut der Ludwig-Maximilians-Universit\u00e4t, M\u00fcnchen, Federal Republic of Germany","institution_ids":["https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I8204097"],"apc_list":null,"apc_paid":null,"fwci":2.7428,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.9244186,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"43","issue":"1","first_page":"118","last_page":"125"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9947999715805054,"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":0.9947999715805054,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9767000079154968,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.9544298052787781},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.8146125078201294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6653422117233276},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6111687421798706},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5378619432449341},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5057899951934814},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0638212263584137}],"concepts":[{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.9544298052787781},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.8146125078201294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6653422117233276},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6111687421798706},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5378619432449341},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5057899951934814},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0638212263584137},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2271954","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271954","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W110027972","https://openalex.org/W132036571","https://openalex.org/W1965517429","https://openalex.org/W1985568000","https://openalex.org/W2003467926","https://openalex.org/W2008889705","https://openalex.org/W2053548136","https://openalex.org/W2084404762","https://openalex.org/W2087185740","https://openalex.org/W4236364473","https://openalex.org/W4253393306"],"related_works":["https://openalex.org/W2089968568","https://openalex.org/W2048273249","https://openalex.org/W2950239705","https://openalex.org/W2261099788","https://openalex.org/W2498880115","https://openalex.org/W1526718205","https://openalex.org/W2735923117","https://openalex.org/W2089427484","https://openalex.org/W2086359902","https://openalex.org/W2115913661"],"abstract_inverted_index":{"By":[0],"[12]":[1],"we":[2,32],"know":[3],"that":[4,35,125],"transfinite":[5,37,167],"induction":[6,38,168],"up":[7,39,174],"to":[8,40,68,131,153,175],"\u0398":[9,45],"\u03b5\u03a9":[10,46],"N":[11,19,24,47,54,62,101,110],"+1":[12,48],"0":[13,49,97],"is":[14,50,87,127,143,163],"not":[15],"provable":[16,51],"in":[17,52,108,139],"ID":[18,53,61,109],",":[20,56,63,121,134,160],"the":[21,57,79,104,113,164],"theory":[22],"of":[23,60,81,166],"-times":[25],"iterated":[26,72],"inductive":[27,73],"definitions.":[28,74],"In":[29,75],"this":[30,66],"paper":[31],"will":[33],"show":[34],"conversely":[36],"any":[41],"ordinal":[42],"less":[43],"than":[44],"i":[55,111],"intuitionistic":[58],"version":[59],"and":[64,96],"extend":[65],"result":[67],"theories":[69],"for":[70],"transfinitely":[71],"[14]":[76],"Sch\u00fctte":[77],"proves":[78],"wellordering":[80,141],"his":[82],"notational":[83],"systems":[84],"using":[85],"predicates":[86,105],"wellordered)":[88],"with":[89,112,129],"M":[90,119,132,156,170],"\u03ba":[91,99,120,133,157,171],"\u2254":[92],"{":[93],"x":[94],"\u2208":[95],"\u2264":[98,100],".":[102,177],"Obviously":[103],"are":[106],"definable":[107],"defining":[114],"axioms:":[115],"where":[116,154],"Prog":[117],"[":[118],"X":[122,126],"]":[123,162],"means":[124],"progressive":[128],"respect":[130],"i.e.":[135],"The":[136],"crucial":[137],"point":[138],"Sch\u00fctte's":[140],"proof":[142],"Lemma":[144],"19":[145],"[14,":[146],"p.":[147],"130]":[148],"which":[149],"can":[150],"be":[151],"modified":[152],"TI[":[155],"+":[158,172],"1":[159,173],"a":[161,176],"scheme":[165],"over":[169]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}