{"id":"https://openalex.org/W3035401974","doi":"https://doi.org/10.1002/malq.202000042","title":"What is effective transfinite recursion in reverse mathematics?","display_name":"What is effective transfinite recursion in reverse mathematics?","publication_year":2020,"publication_date":"2020-12-01","ids":{"openalex":"https://openalex.org/W3035401974","doi":"https://doi.org/10.1002/malq.202000042","mag":"3035401974"},"language":"en","primary_location":{"id":"doi:10.1002/malq.202000042","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.202000042","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.202000042","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.202000042","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Anton Freund","orcid":null},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technical University of Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Anton Freund","raw_affiliation_strings":["Fachbereich Mathematik Technische Universit\u00e4t Darmstadt Schlossgartenstr. 7, 64289 Darmstadt Germany"],"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik Technische Universit\u00e4t Darmstadt Schlossgartenstr. 7, 64289 Darmstadt Germany","institution_ids":["https://openalex.org/I31512782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I31512782"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":{"value":2630,"currency":"USD","value_usd":2630},"fwci":0.4332,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68414903,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"66","issue":"4","first_page":"479","last_page":"483"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.8894000053405762,"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":0.8894000053405762,"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":0.0333000011742115,"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.018699999898672104,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.9606999754905701},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.867900013923645},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6075999736785889},{"id":"https://openalex.org/keywords/double-recursion","display_name":"Double recursion","score":0.5807999968528748},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5715000033378601},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5041000247001648}],"concepts":[{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.9606999754905701},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.867900013923645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7892000079154968},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6075999736785889},{"id":"https://openalex.org/C139503435","wikidata":"https://www.wikidata.org/wiki/Q5300083","display_name":"Double recursion","level":3,"score":0.5807999968528748},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5715000033378601},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5041000247001648},{"id":"https://openalex.org/C124416688","wikidata":"https://www.wikidata.org/wiki/Q3454656","display_name":"Mutual recursion","level":3,"score":0.4896000027656555},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40220001339912415},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34529998898506165},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30660000443458557},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.30390000343322754},{"id":"https://openalex.org/C2778408900","wikidata":"https://www.wikidata.org/wiki/Q1329258","display_name":"Cardinal number (linguistics)","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C71559656","wikidata":"https://www.wikidata.org/wiki/Q671298","display_name":"Divide and conquer algorithms","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2662000060081482},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.260699987411499}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/malq.202000042","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.202000042","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.202000042","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2006.08953","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.08953","pdf_url":"https://arxiv.org/pdf/2006.08953","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:143709","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/143709/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel"}],"best_oa_location":{"id":"doi:10.1002/malq.202000042","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.202000042","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.202000042","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3035401974.pdf","grobid_xml":"https://content.openalex.org/works/W3035401974.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2025460262","https://openalex.org/W2065144039","https://openalex.org/W4229690001","https://openalex.org/W4296119740"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1,52],"the":[2,36,40,53],"context":[3],"of":[4,20,39,62],"reverse":[5],"mathematics,":[6],"effective":[7,63],"transfinite":[8,64],"recursion":[9,23,65],"refers":[10],"to":[11,17,35],"a":[12,59,72],"principle":[13,47],"that":[14,29,45,58],"allows":[15],"us":[16],"construct":[18],"sequences":[19],"sets":[21],"by":[22],"along":[24],"arbitrary":[25],"well":[26],"orders,":[27],"provided":[28],"each":[30],"set":[31],"is":[32,43,48,66,81],"\u2010definable":[33],"relative":[34],"previous":[37],"stages":[38],"recursion.":[41],"It":[42],"known":[44],"this":[46],"provable":[49,83],"in":[50,84],".":[51,85],"present":[54],"note,":[55],"we":[56],"argue":[57],"common":[60],"formulation":[61],"too":[67],"restrictive.":[68],"We":[69],"then":[70],"propose":[71],"more":[73],"liberal":[74],"formulation,":[75],"which":[76],"appears":[77],"very":[78],"natural":[79],"and":[80],"still":[82]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-06-19T00:00:00"}