{"id":"https://openalex.org/W2288602807","doi":"https://doi.org/10.1215/00294527-2018-0020","title":"\u03a010-Encodability and Omniscient Reductions","display_name":"\u03a010-Encodability and Omniscient Reductions","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2288602807","doi":"https://doi.org/10.1215/00294527-2018-0020","mag":"2288602807"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-2018-0020","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2018-0020","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-60/issue-1/%ce%a010-Encodability-and-Omniscient-Reductions/10.1215/00294527-2018-0020.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-60/issue-1/%ce%a010-Encodability-and-Omniscient-Reductions/10.1215/00294527-2018-0020.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Benoit Monin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Benoit Monin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Ludovic Patey","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ludovic Patey","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3992,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.61167107,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"60","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9878000020980835,"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":0.9878000020980835,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.006000000052154064,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.00139999995008111,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6891000270843506},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5084999799728394},{"id":"https://openalex.org/keywords/reverse-mathematics","display_name":"Reverse mathematics","score":0.44920000433921814},{"id":"https://openalex.org/keywords/infinite-set","display_name":"Infinite set","score":0.40790000557899475},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.39649999141693115},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.35019999742507935},{"id":"https://openalex.org/keywords/baire-space","display_name":"Baire space","score":0.3255000114440918},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.30570000410079956}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8801000118255615},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6891000270843506},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5152999758720398},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5084999799728394},{"id":"https://openalex.org/C127753061","wikidata":"https://www.wikidata.org/wiki/Q2005236","display_name":"Reverse mathematics","level":3,"score":0.44920000433921814},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.40790000557899475},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.39649999141693115},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.35019999742507935},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35010001063346863},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32989999651908875},{"id":"https://openalex.org/C166359235","wikidata":"https://www.wikidata.org/wiki/Q1150180","display_name":"Baire space","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C44659138","wikidata":"https://www.wikidata.org/wiki/Q1052678","display_name":"Baire category theorem","level":2,"score":0.30559998750686646},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.3043999969959259},{"id":"https://openalex.org/C188521023","wikidata":"https://www.wikidata.org/wiki/Q6795644","display_name":"Maximal set","level":3,"score":0.30239999294281006},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.2840000092983246},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C189892329","wikidata":"https://www.wikidata.org/wiki/Q2577940","display_name":"Baire measure","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.2700999975204468},{"id":"https://openalex.org/C17327563","wikidata":"https://www.wikidata.org/wiki/Q1991405","display_name":"Nowhere dense set","level":3,"score":0.26190000772476196}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1215/00294527-2018-0020","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2018-0020","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-60/issue-1/%ce%a010-Encodability-and-Omniscient-Reductions/10.1215/00294527-2018-0020.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1603.01086","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.01086","pdf_url":"https://arxiv.org/pdf/1603.01086","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.ndjfl/1547802298","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1547802298","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:HAL:hal-03362579v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03362579","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Notre Dame Journal of Formal Logic, 2019, 60 (1), pp.1--12. &#x27E8;10.1215/00294527-2018-0020&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1215/00294527-2018-0020","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2018-0020","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-60/issue-1/%ce%a010-Encodability-and-Omniscient-Reductions/10.1215/00294527-2018-0020.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306193","display_name":"John Templeton Foundation","ror":"https://ror.org/035tnyy05"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2288602807.pdf","grobid_xml":"https://content.openalex.org/works/W2288602807.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1574049752","https://openalex.org/W1579696469","https://openalex.org/W1757113349","https://openalex.org/W1984983426","https://openalex.org/W1999737391","https://openalex.org/W2016125425","https://openalex.org/W2047601400","https://openalex.org/W2058683290","https://openalex.org/W2070956093","https://openalex.org/W2071956244","https://openalex.org/W2082065673","https://openalex.org/W2112673210","https://openalex.org/W2131443763","https://openalex.org/W2148962283","https://openalex.org/W2161105128","https://openalex.org/W2170311001","https://openalex.org/W2215415851","https://openalex.org/W2474654837","https://openalex.org/W2962720709","https://openalex.org/W2963638240","https://openalex.org/W2963693343","https://openalex.org/W4233662453","https://openalex.org/W4239407195","https://openalex.org/W4246804796","https://openalex.org/W4296119740"],"related_works":[],"abstract_inverted_index":{"A":[0,4],"set":[1,11],"of":[2,12,23,41,46,87],"integers":[3,13],"is":[5,75],"computably":[6,26,78],"encodable":[7,27],"if":[8],"every":[9],"infinite":[10,16],"has":[14],"an":[15],"subset":[17],"computing":[18],"A.":[19],"By":[20],"a":[21,61,85],"result":[22],"Solovay,":[24],"the":[25,31,47,53],"sets":[28,56],"are":[29],"exactly":[30],"hyperarithmetic":[32],"ones.":[33],"In":[34],"this":[35,39,66],"article,":[36],"we":[37,51,68],"extend":[38],"notion":[40],"computable":[42],"encodability":[43],"to":[44,65,80],"subsets":[45],"Baire":[48],"space,":[49],"and":[50,89],"characterize":[52],"\u03a010-encodable":[54],"compact":[55],"as":[57],"those":[58],"which":[59],"admit":[60],"nonempty":[62],"\u03a311-subset.":[63],"Thanks":[64],"equivalence,":[67],"prove":[69],"that":[70],"weak":[71,72],"K\u00f6nig\u2019s":[73],"lemma":[74],"not":[76],"strongly":[77],"reducible":[79],"Ramsey\u2019s":[81],"theorem.":[82],"This":[83],"answers":[84],"question":[86],"Hirschfeldt":[88],"Jockusch.":[90]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
