{"id":"https://openalex.org/W2519087744","doi":"https://doi.org/10.1007/s00012-017-0465-9","title":"On the local closure of clones on countable sets","display_name":"On the local closure of clones on countable sets","publication_year":2017,"publication_date":"2017-10-22","ids":{"openalex":"https://openalex.org/W2519087744","doi":"https://doi.org/10.1007/s00012-017-0465-9","mag":"2519087744"},"language":"en","primary_location":{"id":"doi:10.1007/s00012-017-0465-9","doi":"https://doi.org/10.1007/s00012-017-0465-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00012-017-0465-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00012-017-0465-9.pdf","source":{"id":"https://openalex.org/S178702154","display_name":"Algebra Universalis","issn_l":"0002-5240","issn":["0002-5240","0002-5270","1420-8911"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algebra universalis","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00012-017-0465-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049007874","display_name":"Erhard Aichinger","orcid":"https://orcid.org/0000-0001-8998-4138","observed_orcids":["https://orcid.org/0000-0001-8998-4138"]},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Erhard Aichinger","raw_affiliation_strings":["Institute for Algebra, Johannes Kepler University Linz, 4040, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Algebra, Johannes Kepler University Linz, 4040, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049007874"],"corresponding_institution_ids":["https://openalex.org/I121883995"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":{"value":3190,"currency":"USD","value_usd":3190},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00938834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"78","issue":"3","first_page":"355","last_page":"361"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.8300999999046326,"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":0.8300999999046326,"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":0.14970000088214874,"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/T12504","display_name":"Mathematics and Applications","score":0.003800000064074993,"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/clones","display_name":"clones","score":0.9629999995231628},{"id":"https://openalex.org/keywords/countable-sets","display_name":"countable sets","score":0.8109999895095825},{"id":"https://openalex.org/keywords/local-closure","display_name":"local closure","score":0.9120000004768372},{"id":"https://openalex.org/keywords/invariant-relations","display_name":"invariant relations","score":0.9359999895095825},{"id":"https://openalex.org/keywords/polymorphism","display_name":"polymorphism","score":0.6140000224113464},{"id":"https://openalex.org/keywords/algebraic-logic","display_name":"algebraic logic","score":0.460999995470047}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9014000296592712},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.7810999751091003},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6593000292778015},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5679000020027161},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5489000082015991},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.4708000123500824},{"id":"https://openalex.org/C198800484","wikidata":"https://www.wikidata.org/wiki/Q1503423","display_name":"Quasigroup","level":2,"score":0.4571000039577484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4271000027656555},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41850000619888306},{"id":"https://openalex.org/C81089528","wikidata":"https://www.wikidata.org/wiki/Q5134986","display_name":"clone (Java method)","level":3,"score":0.40959998965263367},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.367000013589859},{"id":"https://openalex.org/C160771489","wikidata":"https://www.wikidata.org/wiki/Q10564851","display_name":"Closure operator","level":3,"score":0.2773999869823456},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2736999988555908},{"id":"https://openalex.org/C117354338","wikidata":"https://www.wikidata.org/wiki/Q1165112","display_name":"Singleton","level":3,"score":0.2687000036239624},{"id":"https://openalex.org/C162362422","wikidata":"https://www.wikidata.org/wiki/Q1363919","display_name":"Second-countable space","level":3,"score":0.257099986076355},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.2529999911785126}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00012-017-0465-9","doi":"https://doi.org/10.1007/s00012-017-0465-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00012-017-0465-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00012-017-0465-9.pdf","source":{"id":"https://openalex.org/S178702154","display_name":"Algebra Universalis","issn_l":"0002-5240","issn":["0002-5240","0002-5270","1420-8911"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algebra universalis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1609.03722","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.03722","pdf_url":"https://arxiv.org/pdf/1609.03722","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"pmh:oai:epub.jku.at/:3419981","doi":null,"is_oa":true,"landing_page_url":"https://epub.jku.at/doi/10.1007/s00012-017-0465-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401788","display_name":"University Library Linz repository (Johannes Kepler Universitat Linz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I121883995","host_organization_name":"Johannes Kepler University of Linz","host_organization_lineage":["https://openalex.org/I121883995"],"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":"","raw_type":"Text"},{"id":"doi:10.48550/arxiv.1609.03722","doi":"https://doi.org/10.48550/arxiv.1609.03722","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1609.03722","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"}],"best_oa_location":{"id":"doi:10.1007/s00012-017-0465-9","doi":"https://doi.org/10.1007/s00012-017-0465-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00012-017-0465-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00012-017-0465-9.pdf","source":{"id":"https://openalex.org/S178702154","display_name":"Algebra Universalis","issn_l":"0002-5240","issn":["0002-5240","0002-5270","1420-8911"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algebra universalis","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2519087744.pdf","grobid_xml":"https://content.openalex.org/works/W2519087744.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1571096293","https://openalex.org/W2073711166","https://openalex.org/W2084944875","https://openalex.org/W2133585348","https://openalex.org/W2504299149","https://openalex.org/W4293176479"],"related_works":[],"abstract_inverted_index":{"We":[0],"consider":[1],"clones":[2],"on":[3],"countable":[4],"sets.":[5],"If":[6],"such":[7,28],"a":[8,21],"clone":[9],"has":[10],"quasigroup":[11],"operations,":[12],"is":[13,20,35],"locally":[14],"closed":[15],"and":[16],"countable,":[17],"then":[18],"there":[19],"function":[22],"$${f":[23],":":[24],"\\mathbb{N}":[25],"\\rightarrow":[26],"\\mathbb{N}}$$":[27],"that":[29],"the":[30,38,52],"n-ary":[31,39],"part":[32,40],"of":[33,41,54,58],"C":[34],"equal":[36],"to":[37],"Pol":[42],"$${{\\rm":[43,48],"Inv}^{[f(n)]}":[44,49],"C}$$":[45,50],",":[46],"where":[47],"denotes":[51],"set":[53],"f(n)-ary":[55],"invariant":[56],"relations":[57],"C.":[59]},"counts_by_year":[],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-09-23T00:00:00"}