{"id":"https://openalex.org/W4313309371","doi":"https://doi.org/10.1007/s00153-022-00860-4","title":"Some implications of Ramsey Choice for families of $$\\varvec{n}$$-element sets","display_name":"Some implications of Ramsey Choice for families of $$\\varvec{n}$$-element sets","publication_year":2022,"publication_date":"2022-12-16","ids":{"openalex":"https://openalex.org/W4313309371","doi":"https://doi.org/10.1007/s00153-022-00860-4"},"language":"en","primary_location":{"id":"doi:10.1007/s00153-022-00860-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-022-00860-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-022-00860-4.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00153-022-00860-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006815009","display_name":"Lorenz Halbe\u0131sen","orcid":"https://orcid.org/0000-0001-6078-7237"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Lorenz Halbeisen","raw_affiliation_strings":["Department of Mathematics, ETH Zentrum, R\u00e4mistrasse 101, 8092, Z\u00fcrich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0001-6078-7237","affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Zentrum, R\u00e4mistrasse 101, 8092, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034151777","display_name":"Salome Schumacher","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Salome Schumacher","raw_affiliation_strings":["Department of Mathematics, ETH Zentrum, R\u00e4mistrasse 101, 8092, Z\u00fcrich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Zentrum, R\u00e4mistrasse 101, 8092, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006815009"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.3902,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6109348,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"62","issue":"5-6","first_page":"703","last_page":"733"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9911999702453613,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9911999702453613,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9664000272750854,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/algorithm","display_name":"Algorithm","score":0.5359962582588196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2500859498977661}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5359962582588196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2500859498977661}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00153-022-00860-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-022-00860-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-022-00860-4.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/589949","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/589949","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Archive for Mathematical Logic, 62 (5-6)","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.3929/ethz-b-000589949","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000589949","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s00153-022-00860-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-022-00860-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-022-00860-4.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321652","display_name":"Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich","ror":"https://ror.org/05a28rw58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4313309371.pdf","grobid_xml":"https://content.openalex.org/works/W4313309371.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W573961896","https://openalex.org/W1532413719","https://openalex.org/W1991515818","https://openalex.org/W2904756839","https://openalex.org/W2991696797","https://openalex.org/W3132793433"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2317200988","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2947381795"],"abstract_inverted_index":{"Abstract":[0],"For":[1,30,101],"$$n\\in":[2],"\\omega":[3,215],"$$":[4,216],"<mml:math":[5,19,42,57,90,119,135,145,158,175,184,197,217,239,258,292,311,347],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[6,20,43,58,91,120,136,146,159,176,185,198,218,240,259,293,312,348],"<mml:mrow>":[7,44,59,61,70,121,219,241,294,313,349],"<mml:mi>n</mml:mi>":[8,23,66,80,94,139,149,162,188,201,222,249],"<mml:mo>\u2208</mml:mo>":[9,223],"<mml:mi>\u03c9</mml:mi>":[10,224],"</mml:mrow>":[11,48,65,82,83,125,225,252,305,324],"</mml:math>":[12,25,49,84,97,126,142,152,165,178,191,204,226,253,261,306,325],",":[13,166,326],"the":[14,99,154,171,207,235,266,276],"weak":[15],"choice":[16,52,87,129,132],"principle":[17,88],"$$\\textrm{RC}_n$$":[18],"<mml:msub>":[21,242,295,314,350],"<mml:mtext>RC</mml:mtext>":[22,243,296,315,351],"</mml:msub>":[24,245,298,317,353],"is":[26,36,111,179],"defined":[27],"as":[28,156],"follows:":[29],"every":[31,102],"infinite":[32,38,103,113],"set":[33],"X":[34],"there":[35,110],"an":[37,112],"subset":[39],"$$Y\\subseteq":[40],"X$$":[41],"<mml:mi>Y</mml:mi>":[45,63,74],"<mml:mo>\u2286</mml:mo>":[46,73,123],"<mml:mi>X</mml:mi>":[47],"with":[50,127],"a":[51,128,230],"function":[53],"on":[54],"$$[Y]^n:=\\{z\\subseteq":[55],"Y:|z|=n\\}$$":[56],"<mml:msup>":[60],"<mml:mo>[</mml:mo>":[62],"<mml:mo>]</mml:mo>":[64],"</mml:msup>":[67],"<mml:mo>:</mml:mo>":[68,75],"<mml:mo>=</mml:mo>":[69,79],"<mml:mo>{</mml:mo>":[71],"<mml:mi>z</mml:mi>":[72,77],"<mml:mo>|</mml:mo>":[76,78],"<mml:mo>}</mml:mo>":[81],".":[85,262],"The":[86,131],"$$\\textrm{C}_n^-$$":[89,157],"<mml:msubsup>":[92,137,147,160,186,199,247,300,319,355],"<mml:mtext>C</mml:mtext>":[93,161,320],"<mml:mo>-</mml:mo>":[95,140,150,163,189,202,250,303,322],"</mml:msubsup>":[96,141,151,164,190,203,251,304,323],"states":[98],"following:":[100],"family":[104,172],"of":[105,210,233],"n":[106],"-":[107],"element":[108],"sets,":[109],"subfamily":[114],"$${\\mathcal":[115,173],"{G}}\\subseteq":[116],"{\\mathcal":[117],"{F}}$$":[118,174],"<mml:mi>G</mml:mi>":[122],"<mml:mi>F</mml:mi>":[124,177],"function.":[130],"principles":[133],"$$\\textrm{LOC}_n^-$$":[134,183],"<mml:mtext>LOC</mml:mtext>":[138,187,301],"and":[143,307,333],"$$\\textrm{WOC}_n^-$$":[144,196],"<mml:mtext>WOC</mml:mtext>":[148,200,248],"are":[153],"same":[155],"but":[167],"we":[168,227,279,286,341],"assume":[169],"that":[170,289,308,344],"linearly":[180],"orderable":[181],"(for":[182,195],")":[192],"or":[193],"well-orderable":[194],").":[205],"In":[206,275,284],"first":[208],"part":[209],"this":[211],"paper,":[212],"for":[213],"$$m,n\\in":[214],"<mml:mi>m</mml:mi>":[220,244],"<mml:mo>,</mml:mo>":[221],"will":[228,264,280,287,342],"give":[229],"full":[231],"characterization":[232],"when":[234],"implication":[236],"$$\\textrm{RC}_m\\Rightarrow":[237],"\\textrm{WOC}_n^-$$":[238],"<mml:mo>\u21d2</mml:mo>":[246,299,318,354],"holds":[254],"in":[255],"$${\\textsf":[256],"{ZF}}$$":[257],"<mml:mi>ZF</mml:mi>":[260],"We":[263],"prove":[265],"independence":[267],"results":[268],"by":[269],"using":[270],"suitable":[271],"Fraenkel-Mostowski":[272],"permutation":[273],"models.":[274],"second":[277],"part,":[278],"show":[281,288,343],"some":[282],"generalizations.":[283],"particular,":[285],"$$\\textrm{RC}_5\\Rightarrow":[290],"\\textrm{LOC}_5^-$$":[291],"<mml:mn>5</mml:mn>":[297,302],"$$\\textrm{RC}_6\\Rightarrow":[309,345],"\\textrm{C}_3^-$$":[310],"<mml:mn>6</mml:mn>":[316,352],"<mml:mn>3</mml:mn>":[321],"answering":[327],"two":[328],"open":[329],"questions":[330],"from":[331],"Halbeisen":[332],"Tachtsis":[334],"(Arch":[335],"Math":[336],"Logik":[337],"59(5):583\u2013606,":[338],"2020).":[339],"Furthermore,":[340],"\\textrm{C}_9^-$$":[346]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}