{"id":"https://openalex.org/W2065924123","doi":"https://doi.org/10.2307/421012","title":"Step by Recursive Step: Church's Analysis of Effective Calculability","display_name":"Step by Recursive Step: Church's Analysis of Effective Calculability","publication_year":1997,"publication_date":"1997-06-01","ids":{"openalex":"https://openalex.org/W2065924123","doi":"https://doi.org/10.2307/421012","mag":"2065924123"},"language":"en","primary_location":{"id":"doi:10.2307/421012","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421012","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/A5023409888","display_name":"Wilfried Sieg","orcid":"https://orcid.org/0000-0002-7130-0524"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wilfried Sieg","raw_affiliation_strings":["Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA.E-mail:","Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA. E-mail/i: sieg@cmu.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA.E-mail:","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA. E-mail/i: sieg@cmu.edu","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023409888"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":1.5539,"has_fulltext":false,"cited_by_count":176,"citation_normalized_percentile":{"value":0.8296424,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"3","issue":"2","first_page":"154","last_page":"180"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9797000288963318,"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"}},{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.9753999710083008,"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/dedekind-cut","display_name":"Dedekind cut","score":0.8051961660385132},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5796137452125549},{"id":"https://openalex.org/keywords/period","display_name":"Period (music)","score":0.5780046582221985},{"id":"https://openalex.org/keywords/analogy","display_name":"Analogy","score":0.5654245615005493},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.5430717468261719},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.5255852341651917},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.5251098275184631},{"id":"https://openalex.org/keywords/church-history","display_name":"Church history","score":0.4946705996990204},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.4908028542995453},{"id":"https://openalex.org/keywords/section","display_name":"Section (typography)","score":0.47210779786109924},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.42990168929100037},{"id":"https://openalex.org/keywords/character","display_name":"Character (mathematics)","score":0.42015668749809265},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40007370710372925},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3798367977142334},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35765233635902405},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.3511878550052643},{"id":"https://openalex.org/keywords/history","display_name":"History","score":0.2786411643028259},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16917088627815247},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.157975971698761},{"id":"https://openalex.org/keywords/theology","display_name":"Theology","score":0.1566426157951355},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1549118459224701}],"concepts":[{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.8051961660385132},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5796137452125549},{"id":"https://openalex.org/C2781291010","wikidata":"https://www.wikidata.org/wiki/Q178580","display_name":"Period (music)","level":2,"score":0.5780046582221985},{"id":"https://openalex.org/C521332185","wikidata":"https://www.wikidata.org/wiki/Q185816","display_name":"Analogy","level":2,"score":0.5654245615005493},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.5430717468261719},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.5255852341651917},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.5251098275184631},{"id":"https://openalex.org/C10869588","wikidata":"https://www.wikidata.org/wiki/Q1800439","display_name":"Church history","level":2,"score":0.4946705996990204},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.4908028542995453},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.47210779786109924},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.42990168929100037},{"id":"https://openalex.org/C2780861071","wikidata":"https://www.wikidata.org/wiki/Q1062934","display_name":"Character (mathematics)","level":2,"score":0.42015668749809265},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40007370710372925},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3798367977142334},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35765233635902405},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.3511878550052643},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.2786411643028259},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16917088627815247},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.157975971698761},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"score":0.1566426157951355},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1549118459224701},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C107038049","wikidata":"https://www.wikidata.org/wiki/Q35986","display_name":"Aesthetics","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/421012","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421012","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/1182353501","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1182353501","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":62,"referenced_works":["https://openalex.org/W57213769","https://openalex.org/W91080868","https://openalex.org/W574857009","https://openalex.org/W850599559","https://openalex.org/W1480101973","https://openalex.org/W1483568252","https://openalex.org/W1562318894","https://openalex.org/W1964062928","https://openalex.org/W1971418649","https://openalex.org/W1972347230","https://openalex.org/W1975810242","https://openalex.org/W1986824935","https://openalex.org/W2023778211","https://openalex.org/W2034109862","https://openalex.org/W2040083714","https://openalex.org/W2040094858","https://openalex.org/W2041833446","https://openalex.org/W2063858946","https://openalex.org/W2064811181","https://openalex.org/W2080280205","https://openalex.org/W2081416038","https://openalex.org/W2086727636","https://openalex.org/W2102202685","https://openalex.org/W2111935378","https://openalex.org/W2120488480","https://openalex.org/W2132161762","https://openalex.org/W2132699442","https://openalex.org/W2163568292","https://openalex.org/W2313773479","https://openalex.org/W2313950537","https://openalex.org/W2317985617","https://openalex.org/W2319210160","https://openalex.org/W2320524668","https://openalex.org/W2323777246","https://openalex.org/W2323803659","https://openalex.org/W2325612495","https://openalex.org/W2328992634","https://openalex.org/W2329928786","https://openalex.org/W2331685757","https://openalex.org/W2487450508","https://openalex.org/W2798840070","https://openalex.org/W2932189326","https://openalex.org/W2977904728","https://openalex.org/W3026105695","https://openalex.org/W4234975009","https://openalex.org/W4237625569","https://openalex.org/W4237996176","https://openalex.org/W4240853462","https://openalex.org/W4247319632","https://openalex.org/W4252147174","https://openalex.org/W4254427418","https://openalex.org/W4255132490","https://openalex.org/W4285719527","https://openalex.org/W6623656706","https://openalex.org/W6641292088","https://openalex.org/W6656514167","https://openalex.org/W6672460540","https://openalex.org/W6675189557","https://openalex.org/W6677966447","https://openalex.org/W6679755832","https://openalex.org/W6699863756","https://openalex.org/W6700461227"],"related_works":["https://openalex.org/W4388314147","https://openalex.org/W1494365721","https://openalex.org/W2024325294","https://openalex.org/W140701301","https://openalex.org/W2613737899","https://openalex.org/W2605128783","https://openalex.org/W2500512079","https://openalex.org/W1515240813","https://openalex.org/W6306397","https://openalex.org/W62088930"],"abstract_inverted_index":{"Abstract":[0],"Alonzo":[1],"Church's":[2,124,183],"mathematical":[3],"work":[4],"on":[5,111],"computability":[6],"and":[7,12,96,119,190],"undecidability":[8],"is":[9,38,160],"well-known":[10],"indeed,":[11],"we":[13],"seem":[14],"to":[15,31,68,105,127,143,150],"have":[16],"an":[17,163,197],"excellent":[18],"understanding":[19],"of":[20,74,90,123,130,134,157,187,202],"the":[21,32,100,128,131,151,155,193],"context":[22],"in":[23,52,61,72,86,114,192],"which":[24],"it":[25,56,70],"arose.":[26],"The":[27],"approach":[28],"Church":[29,66,95,170],"took":[30],"underlying":[33],"conceptual":[34],"issues,":[35],"by":[36,162],"contrast,":[37],"less":[39],"well":[40],"understood.":[41],"Why,":[42],"for":[43,166,174],"example,":[44],"was":[45],"\u201cChurch's":[46],"Thesis\u201d":[47],"put":[48],"forward":[49],"publicly":[50],"only":[51],"April":[53],"1935,":[54],"when":[55],"had":[57,84],"been":[58],"formulated":[59],"already":[60],"February/March":[62],"1934?":[63,87],"Why":[64,169],"did":[65],"choose":[67],"formulate":[69],"then":[71],"terms":[73],"G\u00f6del's":[75,172],"general":[76],"recursiveness,":[77],"not":[78],"his":[79,175],"own":[80],"\u03bb-definability":[81],"as":[82],"he":[83],"done":[85],"A":[88],"number":[89],"letters":[91],"were":[92],"exchanged":[93],"between":[94],"Paul":[97],"Bernays":[98],"during":[99,116],"period":[101,118],"from":[102],"December":[103],"1934":[104],"August":[106],"1937;":[107],"they":[108,140],"throw":[109],"light":[110],"critical":[112],"developments":[113],"Princeton":[115],"that":[117,186],"reveal":[120],"novel":[121],"aspects":[122],"distinctive":[125],"contribution":[126],"analysis":[129,184],"informal":[132],"notion":[133],"effective":[135],"calculability":[136],".":[137,177],"In":[138,178],"particular,":[139],"allow":[141],"me":[142],"give":[144],"informed,":[145],"though":[146],"still":[147],"tentative":[148],"answers":[149,159],"questions":[152],"I":[153,181],"raised;":[154],"character":[156],"my":[158],"reflected":[161],"alternative":[164],"title":[165],"this":[167],"paper,":[168],"needed":[171],"recursiveness":[173],"Thesis":[176],"Section":[179],"5,":[180],"contrast":[182],"with":[185,199],"Alan":[188],"Turing":[189],"explore,":[191],"very":[194],"last":[195],"section,":[196],"analogy":[198],"Dedekind's":[200],"investigation":[201],"continuity.":[203]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":22},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2026-05-13T08:25:38.343686","created_date":"2025-10-10T00:00:00"}
