{"id":"https://openalex.org/W1833353700","doi":"https://doi.org/10.3233/com-160067","title":"Coloring the rationals in reverse mathematics","display_name":"Coloring the rationals in reverse mathematics","publication_year":2016,"publication_date":"2016-09-06","ids":{"openalex":"https://openalex.org/W1833353700","doi":"https://doi.org/10.3233/com-160067","mag":"1833353700"},"language":"en","primary_location":{"id":"doi:10.3233/com-160067","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-160067","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1508.00752","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078323773","display_name":"Emanuele Frittaion","orcid":"https://orcid.org/0000-0003-4965-9271"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Emanuele Frittaion","raw_affiliation_strings":["Mathematical Institute, Tohoku University, Japan. \u00a0","Mathematical Institute, Tohoku University, Japan. frittaion@math.tohoku.ac.jp;\u00a0"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Tohoku University, Japan. \u00a0","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Mathematical Institute, Tohoku University, Japan. frittaion@math.tohoku.ac.jp;\u00a0","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032131260","display_name":"Ludovic Patey","orcid":"https://orcid.org/0000-0002-0304-7926"},"institutions":[{"id":"https://openalex.org/I169173203","display_name":"D\u00e9l\u00e9gation Paris 7","ror":"https://ror.org/00bw5n526","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488","https://openalex.org/I169173203"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Ludovic Patey","raw_affiliation_strings":["Laboratoire PPS, Paris Diderot University, France. \u00a0","Institut de Recherche en Informatique Fondamentale"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire PPS, Paris Diderot University, France. \u00a0","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I169173203"]},{"raw_affiliation_string":"Institut de Recherche en Informatique Fondamentale","institution_ids":["https://openalex.org/I4210117673"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032131260","https://openalex.org/A5078323773"],"corresponding_institution_ids":["https://openalex.org/I169173203","https://openalex.org/I201537933","https://openalex.org/I204730241","https://openalex.org/I4210117673"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00578714,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":"4","first_page":"319","last_page":"331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9980000257492065,"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":0.9884999990463257,"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/rational-number","display_name":"Rational number","score":0.7885414958000183},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7697879076004028},{"id":"https://openalex.org/keywords/ramsey-theory","display_name":"Ramsey theory","score":0.7185814380645752},{"id":"https://openalex.org/keywords/ramseys-theorem","display_name":"Ramsey's theorem","score":0.6692942976951599},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6315670013427734},{"id":"https://openalex.org/keywords/reverse-mathematics","display_name":"Reverse mathematics","score":0.6222205758094788},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5992614030838013},{"id":"https://openalex.org/keywords/order-type","display_name":"Order type","score":0.5683208107948303},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5408227443695068},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.506229817867279},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4940200448036194},{"id":"https://openalex.org/keywords/monochromatic-color","display_name":"Monochromatic color","score":0.46807679533958435},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43077558279037476},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08887547254562378},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.05828025937080383}],"concepts":[{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.7885414958000183},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7697879076004028},{"id":"https://openalex.org/C112291201","wikidata":"https://www.wikidata.org/wiki/Q1336170","display_name":"Ramsey theory","level":2,"score":0.7185814380645752},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.6692942976951599},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6315670013427734},{"id":"https://openalex.org/C127753061","wikidata":"https://www.wikidata.org/wiki/Q2005236","display_name":"Reverse mathematics","level":3,"score":0.6222205758094788},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5992614030838013},{"id":"https://openalex.org/C138890893","wikidata":"https://www.wikidata.org/wiki/Q620006","display_name":"Order type","level":2,"score":0.5683208107948303},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5408227443695068},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.506229817867279},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4940200448036194},{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.46807679533958435},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43077558279037476},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08887547254562378},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.05828025937080383},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3233/com-160067","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-160067","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},{"id":"pmh:oai:eprints.whiterose.ac.uk:138942","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1508.00752","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.00752","pdf_url":"https://arxiv.org/pdf/1508.00752","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":"","raw_type":"text"},{"id":"mag:1833353700","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1508.00752.pdf","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:HAL:hal-01888756v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01888756","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computability, 2017, 6 (4), pp.319 - 331. ⟨10.3233/COM-160067⟩","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1508.00752","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1508.00752","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1508.00752","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.00752","pdf_url":"https://arxiv.org/pdf/1508.00752","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1622490310","https://openalex.org/W1996516812","https://openalex.org/W2000565016","https://openalex.org/W2016125425","https://openalex.org/W2026779741","https://openalex.org/W2032211530","https://openalex.org/W2057392475","https://openalex.org/W2058687150","https://openalex.org/W2078669210","https://openalex.org/W2131443763","https://openalex.org/W2148962283","https://openalex.org/W2170311001","https://openalex.org/W4229690001","https://openalex.org/W4231202900","https://openalex.org/W4238689220"],"related_works":["https://openalex.org/W2963961606","https://openalex.org/W2949231378","https://openalex.org/W2157945276","https://openalex.org/W2230984504","https://openalex.org/W2060782772","https://openalex.org/W1984983426","https://openalex.org/W2964070035","https://openalex.org/W3100726716","https://openalex.org/W3040572287","https://openalex.org/W2016227329","https://openalex.org/W2809716991","https://openalex.org/W3181650468","https://openalex.org/W3098647228","https://openalex.org/W3207152999","https://openalex.org/W2926279489","https://openalex.org/W2799287367","https://openalex.org/W2160285120","https://openalex.org/W2963847608","https://openalex.org/W1795077030","https://openalex.org/W2037609605"],"abstract_inverted_index":{"Ramsey\u2019s":[0,26,83],"theorem":[1,27,69,84,93],"for":[2,28,85,94],"pairs":[3,10,29,42],"asserts":[4],"that":[5,37],"every":[6,38],"2-coloring":[7,39],"of":[8,11,25,40,43,55,65,100],"the":[9,41,62,66,78,91],"integers":[12],"has":[13,45],"an":[14,47],"infinite":[15,48],"monochromatic":[16],"subset.":[17],"In":[18],"this":[19],"paper,":[20],"we":[21],"study":[22],"a":[23,52,71,98,107],"strengthening":[24],"due":[30],"to":[31,74,97],"Erd\u0151s":[32],"and":[33,82],"Rado,":[34],"which":[35],"states":[36],"rationals":[44],"either":[46],"0-homogeneous":[49],"set":[50,54],"or":[51],"1-homogeneous":[53],"order":[56,63],"type":[57,64],"\u03b7,":[58],"where":[59],"\u03b7":[60],"is":[61,70],"rationals.":[67],"This":[68,87],"natural":[72],"candidate":[73],"lie":[75],"strictly":[76],"between":[77],"arithmetic":[79],"comprehension":[80],"axiom":[81],"pairs.":[86],"Erd\u0151s\u2013Rado":[88],"theorem,":[89],"like":[90],"tree":[92],"pairs,":[95],"belongs":[96],"family":[99],"Ramsey-type":[101],"statements":[102],"whose":[103],"logical":[104],"strength":[105],"remains":[106],"challenge.":[108]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}