{"id":"https://openalex.org/W3208376955","doi":"https://doi.org/10.3390/sym13112028","title":"Finitely Supported Binary Relations between Infinite Atomic Sets","display_name":"Finitely Supported Binary Relations between Infinite Atomic Sets","publication_year":2021,"publication_date":"2021-10-27","ids":{"openalex":"https://openalex.org/W3208376955","doi":"https://doi.org/10.3390/sym13112028","mag":"3208376955"},"language":"en","primary_location":{"id":"doi:10.3390/sym13112028","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112028","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2028/pdf?version=1635322342","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/11/2028/pdf?version=1635322342","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064433688","display_name":"Andrei Alexandru","orcid":"https://orcid.org/0000-0002-0563-8391"},"institutions":[{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Andrei Alexandru","raw_affiliation_strings":["Institute of Computer Science, Romanian Academy, 700505 Ia\u015fi, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Romanian Academy, 700505 Ia\u015fi, Romania","institution_ids":["https://openalex.org/I58077936"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072509898","display_name":"Gabriel Ciobanu","orcid":"https://orcid.org/0000-0002-8166-9456"},"institutions":[{"id":"https://openalex.org/I138164181","display_name":"Alexandru Ioan Cuza University","ror":"https://ror.org/022kvet57","country_code":"RO","type":"education","lineage":["https://openalex.org/I138164181"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Gabriel Ciobanu","raw_affiliation_strings":["Faculty of Computer Science, Alexandru Ioan Cuza University, 700506 Ia\u015fi, Romania"],"raw_orcid":"https://orcid.org/0000-0002-8166-9456","affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, Alexandru Ioan Cuza University, 700506 Ia\u015fi, Romania","institution_ids":["https://openalex.org/I138164181"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5072509898"],"corresponding_institution_ids":["https://openalex.org/I138164181"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19204709,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"11","first_page":"2028","last_page":"2028"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9994999766349792,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9994999766349792,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9984999895095825,"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":0.9975000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7185513973236084},{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.6878834962844849},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6272842884063721},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.547118604183197},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.48267629742622375},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.47779518365859985},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.47644713521003723},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44769445061683655},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.4357690215110779},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4340037405490875},{"id":"https://openalex.org/keywords/infinite-set","display_name":"Infinite set","score":0.4206595718860626},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3763815760612488},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.28334105014801025},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12450212240219116},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1160849928855896},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11049070954322815}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7185513973236084},{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.6878834962844849},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6272842884063721},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.547118604183197},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48267629742622375},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.47779518365859985},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.47644713521003723},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44769445061683655},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.4357690215110779},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4340037405490875},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.4206595718860626},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3763815760612488},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.28334105014801025},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12450212240219116},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1160849928855896},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11049070954322815},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13112028","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112028","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2028/pdf?version=1635322342","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:9c4e0bdf31f54a5aa85b112a5c6a13a9","is_oa":true,"landing_page_url":"https://doaj.org/article/9c4e0bdf31f54a5aa85b112a5c6a13a9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 11, p 2028 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/11/2028/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13112028","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry; Volume 13; Issue 11; Pages: 2028","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13112028","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112028","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2028/pdf?version=1635322342","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3208376955.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W755158540","https://openalex.org/W1608084331","https://openalex.org/W1978653019","https://openalex.org/W2007106955","https://openalex.org/W2037026294","https://openalex.org/W2045982128","https://openalex.org/W2064028777","https://openalex.org/W2108640219","https://openalex.org/W2480336574","https://openalex.org/W2606605761","https://openalex.org/W2959537548","https://openalex.org/W2960196423","https://openalex.org/W3125770603","https://openalex.org/W3135277645","https://openalex.org/W3179281489","https://openalex.org/W4239584365","https://openalex.org/W4245071229","https://openalex.org/W4293117209"],"related_works":["https://openalex.org/W2383938896","https://openalex.org/W2901423989","https://openalex.org/W2053726032","https://openalex.org/W2790017930","https://openalex.org/W3125024600","https://openalex.org/W2031218960","https://openalex.org/W2083799093","https://openalex.org/W4298287189","https://openalex.org/W2947386998","https://openalex.org/W3175778664"],"abstract_inverted_index":{"In":[0],"the":[1,10,16,35,65,81,109],"framework":[2,110],"of":[3,12,34,111],"finitely":[4,36,48,57,112],"supported":[5,37,49,77,90,100,113],"atomic":[6,13,42],"sets,":[7],"by":[8],"using":[9],"notion":[11],"cardinality":[14],"and":[15,71],"T-finite":[17],"support":[18],"principle":[19],"(a":[20],"closure":[21],"property":[22],"for":[23],"supports":[24],"in":[25,108],"some":[26,31],"higher-order":[27],"constructions),":[28],"we":[29],"present":[30],"finiteness":[32],"properties":[33],"binary":[38],"relations":[39],"between":[40],"infinite":[41,60,66,78,91,101],"sets.":[43],"Of":[44],"particular":[45],"interest":[46],"are":[47,106],"Dedekind-finite":[50,107],"sets":[51,67,105],"because":[52],"they":[53],"do":[54,73],"not":[55,74,86,96],"contain":[56,75,87,97],"supported,":[58],"countably":[59],"subsets.":[61,79],"We":[62],"prove":[63],"that":[64],"\u2118fs(Ak\u00d7Al),":[68],"\u2118fs(Ak\u00d7\u2118m(A)),":[69],"\u2118fs(\u2118n(A)\u00d7Ak)":[70],"\u2118fs(\u2118n(A)\u00d7\u2118m(A))":[72],"uniformly":[76,89,99],"Moreover,":[80],"functions":[82],"space":[83],"ZAm":[84],"does":[85,95],"a":[88,98],"subset":[92],"whenever":[93],"Z":[94],"subset.":[102],"All":[103],"these":[104],"structures.":[114]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2021-11-08T00:00:00"}