{"id":"https://openalex.org/W2154952077","doi":"https://doi.org/10.2178/bsl/1294186663","title":"Effective Choice and Boundedness Principles in Computable Analysis","display_name":"Effective Choice and Boundedness Principles in Computable Analysis","publication_year":2011,"publication_date":"2011-01-04","ids":{"openalex":"https://openalex.org/W2154952077","doi":"https://doi.org/10.2178/bsl/1294186663","mag":"2154952077"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1294186663","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1294186663","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":"The Bulletin of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0905.4685","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Vasco Brattka","orcid":null},"institutions":[{"id":"https://openalex.org/I157614274","display_name":"University of Cape Town","ror":"https://ror.org/03p74gp79","country_code":"ZA","type":"education","lineage":["https://openalex.org/I157614274"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Vasco Brattka","raw_affiliation_strings":["Laboratory of Foundational Aspects of Computer Science, Department of Mathematics & Applied Mathematics, University of Cape Town, Rondebosch 7701, South AfricaE-mail:"],"affiliations":[{"raw_affiliation_string":"Laboratory of Foundational Aspects of Computer Science, Department of Mathematics & Applied Mathematics, University of Cape Town, Rondebosch 7701, South AfricaE-mail:","institution_ids":["https://openalex.org/I157614274"]}]},{"author_position":"last","author":{"id":null,"display_name":"Guido Gherardi","orcid":null},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Guido Gherardi","raw_affiliation_strings":["Dipartimento Di Filosofia, Universit\u00e0 Di Bologna, ItalyE-mail:"],"affiliations":[{"raw_affiliation_string":"Dipartimento Di Filosofia, Universit\u00e0 Di Bologna, ItalyE-mail:","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157614274"],"apc_list":null,"apc_paid":null,"fwci":6.8365,"has_fulltext":false,"cited_by_count":73,"citation_normalized_percentile":{"value":0.97458002,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"17","issue":"1","first_page":"73","last_page":"117"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9344000220298767,"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":0.9344000220298767,"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":0.021400000900030136,"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/T10126","display_name":"Logic, programming, and type systems","score":0.014399999752640724,"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/computable-analysis","display_name":"Computable analysis","score":0.7494999766349792},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6313999891281128},{"id":"https://openalex.org/keywords/reverse-mathematics","display_name":"Reverse mathematics","score":0.6207000017166138},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5907999873161316},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.42969998717308044},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4016000032424927},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.39399999380111694},{"id":"https://openalex.org/keywords/ultrafilter","display_name":"Ultrafilter","score":0.3671000003814697},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.3653999865055084}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8300999999046326},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.7494999766349792},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6313999891281128},{"id":"https://openalex.org/C127753061","wikidata":"https://www.wikidata.org/wiki/Q2005236","display_name":"Reverse mathematics","level":3,"score":0.6207000017166138},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5907999873161316},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5145000219345093},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.42969998717308044},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4016000032424927},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.39399999380111694},{"id":"https://openalex.org/C87598191","wikidata":"https://www.wikidata.org/wiki/Q1571831","display_name":"Ultrafilter","level":2,"score":0.3671000003814697},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33649998903274536},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C1911482","wikidata":"https://www.wikidata.org/wiki/Q854531","display_name":"Real analysis","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.2745000123977661},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.27399998903274536},{"id":"https://openalex.org/C44659138","wikidata":"https://www.wikidata.org/wiki/Q1052678","display_name":"Baire category theorem","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C93373587","wikidata":"https://www.wikidata.org/wiki/Q335632","display_name":"Mathematical finance","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2178/bsl/1294186663","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1294186663","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":"The Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0905.4685","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0905.4685","pdf_url":"https://arxiv.org/pdf/0905.4685","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:CULeuclid:euclid.bsl/1294186663","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1294186663","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"},{"id":"pmh:oai:cris.unibo.it:11585/104323","is_oa":false,"landing_page_url":"http://hdl.handle.net/11585/104323","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0905.4685","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0905.4685","pdf_url":"https://arxiv.org/pdf/0905.4685","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W96835806","https://openalex.org/W172736740","https://openalex.org/W1497475168","https://openalex.org/W1544955410","https://openalex.org/W1545055820","https://openalex.org/W1556453281","https://openalex.org/W1559786600","https://openalex.org/W1563944230","https://openalex.org/W1590304156","https://openalex.org/W1975917923","https://openalex.org/W1987187730","https://openalex.org/W1991124928","https://openalex.org/W2004000165","https://openalex.org/W2005038809","https://openalex.org/W2005943267","https://openalex.org/W2007915800","https://openalex.org/W2027931514","https://openalex.org/W2031766793","https://openalex.org/W2032551408","https://openalex.org/W2042151572","https://openalex.org/W2045199616","https://openalex.org/W2048516781","https://openalex.org/W2052053709","https://openalex.org/W2055924668","https://openalex.org/W2077769760","https://openalex.org/W2087249699","https://openalex.org/W2087443598","https://openalex.org/W2108709315","https://openalex.org/W2134006590","https://openalex.org/W2141528037","https://openalex.org/W2169019562","https://openalex.org/W2912268883","https://openalex.org/W4233663126","https://openalex.org/W4236134292","https://openalex.org/W4239316923","https://openalex.org/W4243563333","https://openalex.org/W4245716479","https://openalex.org/W4292399988","https://openalex.org/W6617185123"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1,119],"this":[2,36,117,164,196],"paper":[3],"we":[4,19,121,197,213,308,331],"study":[5,122],"a":[6,217,273,280,310],"new":[7,227,281],"approach":[8],"to":[9,14,56,316],"classify":[10],"mathematical":[11],"theorems":[12,25,38,109,123,329],"according":[13],"their":[15,42],"computational":[16,231],"content.":[17],"Basically,":[18],"are":[20,39,45,97],"asking":[21],"the":[22,69,126,130,134,139,144,155,199,230,234,257,292,303,321,324,333],"question":[23],"which":[24,44,96],"can":[26,112,177,252],"be":[27,113,180,253],"continuously":[28],"or":[29,59,247],"computably":[30],"transferred":[31],"into":[32,163],"each":[33],"other?":[34],"For":[35],"purpose":[37],"considered":[40,181],"via":[41],"realizers":[43],"operations":[46,64],"with":[47,204],"certain":[48,80,107,218,285],"input":[49],"and":[50,68,93,102,143,158,175,185,209,212,224,268,298,300,330],"output":[51],"data.":[52],"The":[53],"technical":[54],"tool":[55],"express":[57],"continuous":[58],"computable":[60,269],"relations":[61],"between":[62],"such":[63,83,124,172],"is":[65,222],"Weihrauch":[66,100,183,289,325],"reducibility":[67],"partially":[70],"ordered":[71],"degree":[72,326],"structure":[73],"induced":[74],"by":[75],"it.":[76],"We":[77,148,271],"have":[78],"identified":[79],"choice":[81,92],"principles":[82,168],"as":[84,125,173,182,338],"co-finite":[85],"choice,":[86,88,90,95],"discrete":[87],"interval":[89],"compact":[91],"closed":[94],"cornerstones":[98],"among":[99],"degrees":[101,184],"it":[103,251],"turns":[104],"out":[105,255],"that":[106,215,314],"core":[108],"in":[110,116,191,207,216,256],"analysis":[111],"classified":[114],"naturally":[115,179],"structure.":[118],"particular,":[120],"Intermediate":[127],"Value":[128],"Theorem,":[129,133,138],"Baire":[131,304],"Category":[132,305],"Banach":[135],"Inverse":[136],"Mapping":[137],"Closed":[140],"Graph":[141],"Theorem":[142,157,295,337],"Uniform":[145],"Boundedness":[146],"Theorem.":[147,306],"also":[149,178],"explore":[150],"how":[151],"existing":[152,205],"classifications":[153,206],"of":[154,201,233,259,264,275,288,296,312,323,327],"Hahn\u2013Banach":[156],"Weak":[159],"K\u0151nig's":[160],"Lemma":[161],"fit":[162],"picture.":[165],"Well-known":[166],"omniscience":[167],"from":[169],"constructive":[170,208],"mathematics":[171,211,261],"LPO":[174],"LLPO":[176],"they":[186],"play":[187],"an":[188,339],"important":[189],"role":[190],"our":[192,202,220],"classification.":[193],"Based":[194],"on":[195,229,279,284,291,302],"compare":[198],"results":[200],"classification":[203,221,238,322],"reverse":[210],"claim":[214],"sense":[219],"finer":[223],"sheds":[225],"some":[226],"light":[228],"content":[232],"respective":[235],"theorems.":[236],"Our":[237],"scheme":[239],"does":[240],"not":[241],"require":[242],"any":[243],"particular":[244],"logical":[245],"framework":[246,258],"axiomatic":[248],"setting,":[249],"but":[250],"carried":[254],"classical":[260],"using":[262],"tools":[263],"topology,":[265],"computability":[266],"theory":[267],"analysis.":[270],"develop":[272],"number":[274,311],"separation":[276],"techniques":[277],"based":[278,301],"parallelization":[282],"principle,":[283],"invariance":[286],"properties":[287],"reducibility,":[290],"Low":[293],"Basis":[294],"Jockusch":[297],"Soare":[299],"Finally,":[307],"present":[309],"metatheorems":[313],"allow":[315],"derive":[317],"upper":[318],"bounds":[319],"for":[320],"many":[328],"discuss":[332],"Brouwer":[334],"Fixed":[335],"Point":[336],"example.":[340]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":7}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}