{"id":"https://openalex.org/W2935840641","doi":"https://doi.org/10.1007/s00153-019-00671-0","title":"Construction with opposition: cardinal invariants and games","display_name":"Construction with opposition: cardinal invariants and games","publication_year":2019,"publication_date":"2019-03-22","ids":{"openalex":"https://openalex.org/W2935840641","doi":"https://doi.org/10.1007/s00153-019-00671-0","mag":"2935840641"},"language":"en","primary_location":{"id":"doi:10.1007/s00153-019-00671-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-019-00671-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-019-00671-0.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"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00153-019-00671-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070977261","display_name":"J\u00f6rg Brendle","orcid":"https://orcid.org/0000-0001-8120-2883"},"institutions":[{"id":"https://openalex.org/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"J\u00f6rg Brendle","raw_affiliation_strings":["Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan","institution_ids":["https://openalex.org/I65837984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065080063","display_name":"Michael Hru\u0161\u00e1k","orcid":"https://orcid.org/0000-0002-1692-2216"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Hru\u0161\u00e1k","raw_affiliation_strings":["Centro de Ciencias Matem\u00e1ticas, UNAM, A.P. 61-3, Xangari, 58089, Morelia, Michoac\u00e1n, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Ciencias Matem\u00e1ticas, UNAM, A.P. 61-3, Xangari, 58089, Morelia, Michoac\u00e1n, Mexico","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012280628","display_name":"V\u00edctor Torres-P\u00e9rez","orcid":"https://orcid.org/0000-0002-8928-1894"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"V\u00edctor Torres-P\u00e9rez","raw_affiliation_strings":["Institute of Discrete Mathematics and Geometry, TU Wien, Wiedner Hauptstrasse 8/104, 1040, Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0002-8928-1894","affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics and Geometry, TU Wien, Wiedner Hauptstrasse 8/104, 1040, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012280628"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":1996,"currency":"EUR","value_usd":2152},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.11310173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"58","issue":"7-8","first_page":"943","last_page":"963"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9944000244140625,"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":0.9876999855041504,"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/mathematics","display_name":"Mathematics","score":0.7626348733901978},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5353600978851318},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3278096914291382},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32582780718803406},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17148920893669128}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7626348733901978},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5353600978851318},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3278096914291382},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32582780718803406},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17148920893669128}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00153-019-00671-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-019-00671-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-019-00671-0.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"}],"best_oa_location":{"id":"doi:10.1007/s00153-019-00671-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-019-00671-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-019-00671-0.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":[{"id":"https://openalex.org/G2575382140","display_name":null,"funder_award_id":"P 29860-N35","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3582544167","display_name":"Forcing Theory and the Size of the Continuum","funder_award_id":"15K04977","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G443235634","display_name":null,"funder_award_id":"PAPIIT IN 102311","funder_id":"https://openalex.org/F4320323401","funder_display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico"},{"id":"https://openalex.org/G7380268728","display_name":"Rado\u00b4s Conjecture, the Tree Property, Square Principles and Topology","funder_award_id":"P 26869","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7547124357","display_name":"New aspects of cardinal invariants","funder_award_id":"18K03398","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7727133762","display_name":null,"funder_award_id":"177758","funder_id":"https://openalex.org/F4320321739","funder_display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda"},{"id":"https://openalex.org/G8273096235","display_name":null,"funder_award_id":"15K04977","funder_id":"https://openalex.org/F4320320212","funder_display_name":"Japan Society for the Promotion of Science London"}],"funders":[{"id":"https://openalex.org/F4320320212","display_name":"Japan Society for the Promotion of Science London","ror":"https://ror.org/02m7axw05"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"},{"id":"https://openalex.org/F4320323401","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2935840641.pdf","grobid_xml":"https://content.openalex.org/works/W2935840641.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W72011958","https://openalex.org/W875475425","https://openalex.org/W1512576849","https://openalex.org/W1595388840","https://openalex.org/W1974828116","https://openalex.org/W1980657807","https://openalex.org/W1984742688","https://openalex.org/W1991721857","https://openalex.org/W2013336096","https://openalex.org/W2035501774","https://openalex.org/W2061653255","https://openalex.org/W2087004834","https://openalex.org/W2094657784","https://openalex.org/W2121739804","https://openalex.org/W2122092051","https://openalex.org/W2141123860","https://openalex.org/W2727305049","https://openalex.org/W3043689882","https://openalex.org/W4250968511"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W2976797620","https://openalex.org/W3046926816","https://openalex.org/W3083539681","https://openalex.org/W2530212042","https://openalex.org/W2332694326","https://openalex.org/W4249089511","https://openalex.org/W4287734682"],"abstract_inverted_index":{"We":[0,18],"consider":[1],"several":[2],"game":[3,39,72],"versions":[4,73],"of":[5,74],"the":[6,21,30,44,70],"cardinal":[7,31],"invariants":[8,32],"$${\\mathfrak":[9,12,15,50,54,64,67,75,78,86],"{t}}$$":[10,76],",":[11,80],"{u}}$$":[13,79],"and":[14,53,66,77],"{a}}$$":[16,87],".":[17],"show":[19,48],"that":[20,24,29,37,49],"standard":[22],"proof":[23],"parametrized":[25],"diamond":[26],"principles":[27],"prove":[28],"are":[33,41,57,69],"small":[34],"actually":[35],"shows":[36],"their":[38],"counterparts":[40],"small.":[42],"On":[43],"other":[45],"hand":[46],"we":[47],"{t}}<{\\mathfrak":[51],"{t}}_{Builder}$$":[52,65],"{u}}<{\\mathfrak":[55],"{u}}_{Builder}$$":[56,68],"both":[58],"relatively":[59],"consistent":[60],"with":[61],"ZFC,":[62],"where":[63],"principal":[71],"respectively.":[81],"The":[82],"corresponding":[83],"question":[84],"for":[85],"remains":[88],"open.":[89]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}