{"id":"https://openalex.org/W2275511168","doi":"https://doi.org/10.23638/lmcs-13(3:10)2017","title":"The Independence of Markov's Principle in Type Theory","display_name":"The Independence of Markov's Principle in Type Theory","publication_year":2017,"publication_date":"2017-08-15","ids":{"openalex":"https://openalex.org/W2275511168","doi":"https://doi.org/10.23638/lmcs-13(3:10)2017","mag":"2275511168"},"language":"en","primary_location":{"id":"doi:10.23638/lmcs-13(3:10)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:10)2017","pdf_url":"https://lmcs.episciences.org/3859/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/3859/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087100539","display_name":"Thierry Coquand","orcid":"https://orcid.org/0000-0002-5429-5153"},"institutions":[{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Thierry Coquand","raw_affiliation_strings":["University of Gothenburg"],"affiliations":[{"raw_affiliation_string":"University of Gothenburg","institution_ids":["https://openalex.org/I881427289"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020650323","display_name":"Bassel Mannaa","orcid":"https://orcid.org/0000-0003-0097-6188"},"institutions":[{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Bassel Mannaa","raw_affiliation_strings":["University of Gothenburg"],"affiliations":[{"raw_affiliation_string":"University of Gothenburg","institution_ids":["https://openalex.org/I881427289"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087100539"],"corresponding_institution_ids":["https://openalex.org/I881427289"],"apc_list":null,"apc_paid":null,"fwci":1.2462,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84376309,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"Volume 13, Issue 3","issue":null,"first_page":"18","last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9988999962806702,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9933000206947327,"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":0.9896000027656555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6945704221725464},{"id":"https://openalex.org/keywords/markov-kernel","display_name":"Markov kernel","score":0.607336163520813},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5828664898872375},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5651161670684814},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.5542096495628357},{"id":"https://openalex.org/keywords/markov-property","display_name":"Markov property","score":0.5245038270950317},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4964492917060852},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4377742111682892},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3865235149860382},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36765509843826294},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3433910012245178},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.2939583659172058},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.28222811222076416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23166584968566895}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6945704221725464},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.607336163520813},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5828664898872375},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5651161670684814},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.5542096495628357},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.5245038270950317},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4964492917060852},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4377742111682892},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3865235149860382},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36765509843826294},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3433910012245178},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.2939583659172058},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.28222811222076416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23166584968566895},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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":10,"locations":[{"id":"doi:10.23638/lmcs-13(3:10)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:10)2017","pdf_url":"https://lmcs.episciences.org/3859/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:drops-oai.dagstuhl.de:5993","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.17","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},{"id":"pmh:oai:pure.atira.dk:openaire/b8b594d3-6644-4f93-a521-b6af7edaa388","is_oa":false,"landing_page_url":"https://pure.itu.dk/portal/da/publications/b8b594d3-6644-4f93-a521-b6af7edaa388","pdf_url":null,"source":{"id":"https://openalex.org/S4377196680","display_name":"IT University Of Copenhagen (IT University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83467386","host_organization_name":"IT University of Copenhagen","host_organization_lineage":["https://openalex.org/I83467386"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Coquand, T & Mannaa, B 2017, 'The Independence of Markov's Principle in Type Theory', Logical Methods in Computer Science, vol. 13, no. 3, pp. 1-28. https://doi.org/10.23638/LMCS-13(3:10)2017","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1602.04530","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.04530","pdf_url":"https://arxiv.org/pdf/1602.04530","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":"mag:2275511168","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1602.04530","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:doaj.org/article:b28eb88981ab47c094e916879fb8b14d","is_oa":true,"landing_page_url":"https://doaj.org/article/b28eb88981ab47c094e916879fb8b14d","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 13, Issue 3 (2017)","raw_type":"article"},{"id":"doi:10.48550/arxiv.1602.04530","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1602.04530","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:3105836218","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1602.04530v1","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.4230/lipics.fscd.2016.17","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.fscd.2016.17","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""},{"id":"mag:2963610683","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/conf/rta/fscd2016.html#CoquandM16","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.23638/lmcs-13(3:10)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:10)2017","pdf_url":"https://lmcs.episciences.org/3859/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2275511168.pdf"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1546270920","https://openalex.org/W1575675278","https://openalex.org/W1585676614","https://openalex.org/W1592599574","https://openalex.org/W1853838474","https://openalex.org/W1978413491","https://openalex.org/W1980939032","https://openalex.org/W2033146968","https://openalex.org/W2058174669","https://openalex.org/W2067914884","https://openalex.org/W2115456387","https://openalex.org/W2118041160","https://openalex.org/W2149837936","https://openalex.org/W2211030347","https://openalex.org/W2314692902","https://openalex.org/W2499105636","https://openalex.org/W2579485446"],"related_works":["https://openalex.org/W3105836218","https://openalex.org/W2398348021","https://openalex.org/W2055173861","https://openalex.org/W2077553323","https://openalex.org/W2008160048","https://openalex.org/W2279101113","https://openalex.org/W2553076207","https://openalex.org/W2503163003","https://openalex.org/W2971784863","https://openalex.org/W2118233610","https://openalex.org/W2500046133","https://openalex.org/W2136875675","https://openalex.org/W2175833819","https://openalex.org/W2949151551","https://openalex.org/W2199876614","https://openalex.org/W2092003388","https://openalex.org/W3048817003","https://openalex.org/W1562779248","https://openalex.org/W1509432714","https://openalex.org/W3045338440"],"abstract_inverted_index":{"In":[0],"this":[1,25,57,88,100],"paper,":[2],"we":[3,60],"show":[4,84],"that":[5,30,105],"Markov's":[6,31,47,94],"principle":[7,32,48,95],"is":[8],"not":[9,34,50,97],"derivable":[10],"in":[11,36,99,110],"dependent":[12],"type":[13,41,65,70,111],"theory":[14,42,71],"with":[15],"natural":[16],"numbers":[17],"and":[18,102],"one":[19],"universe.":[20],"One":[21],"way":[22],"to":[23,28],"prove":[24],"would":[26],"be":[27,108],"remark":[29],"does":[33,49,96],"hold":[35,51,98],"a":[37,76,91],"sheaf":[38],"model":[39],"of":[40,56,64,75,79,87],"over":[43],"Cantor":[44,80],"space,":[45],"since":[46],"for":[52],"the":[53,73,85],"generic":[54,77],"point":[55,78],"model.":[58],"Instead":[59],"design":[61],"an":[62],"extension":[63,89],"theory,":[66],"which":[67],"intuitively":[68],"extends":[69],"by":[72,90],"addition":[74],"space.":[81],"We":[82],"then":[83],"consistency":[86],"normalization":[92],"argument.":[93],"extension,":[101],"it":[103,106],"follows":[104],"cannot":[107],"proved":[109],"theory.":[112]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}