{"id":"https://openalex.org/W2109908460","doi":"https://doi.org/10.1007/s11225-013-9499-y","title":"Relation Formulas for Protoalgebraic Equality Free Quasivarieties; Pa\u0142asi\u0144ska\u2019s Theorem Revisited","display_name":"Relation Formulas for Protoalgebraic Equality Free Quasivarieties; Pa\u0142asi\u0144ska\u2019s Theorem Revisited","publication_year":2013,"publication_date":"2013-07-17","ids":{"openalex":"https://openalex.org/W2109908460","doi":"https://doi.org/10.1007/s11225-013-9499-y","mag":"2109908460"},"language":"en","primary_location":{"id":"doi:10.1007/s11225-013-9499-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-013-9499-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-013-9499-y.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"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":"Studia Logica","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/s11225-013-9499-y.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064267281","display_name":"A. M. Nurakunov","orcid":"https://orcid.org/0000-0002-3363-9674"},"institutions":[{"id":"https://openalex.org/I10232997","display_name":"L. N. Gumilyov Eurasian National University","ror":"https://ror.org/0242cby63","country_code":"KZ","type":"education","lineage":["https://openalex.org/I10232997"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["CZ","KZ"],"is_corresponding":false,"raw_author_name":"Anvar M. Nurakunov","raw_affiliation_strings":["Eurasian National University, Astana, Kazakhstan","Institute of Mathematics, National Academy of Science, Bishkek, Kyrghyz Republic"],"affiliations":[{"raw_affiliation_string":"Eurasian National University, Astana, Kazakhstan","institution_ids":["https://openalex.org/I10232997"]},{"raw_affiliation_string":"Institute of Mathematics, National Academy of Science, Bishkek, Kyrghyz Republic","institution_ids":["https://openalex.org/I4210120266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075820635","display_name":"Micha\u0142 M. Stronkowski","orcid":"https://orcid.org/0000-0001-6438-6262"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]},{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ","PL"],"is_corresponding":true,"raw_author_name":"Micha\u0142 M. Stronkowski","raw_affiliation_strings":["Eduard \u010cech Center, Charles University, Prague, Czech Republic","Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Eduard \u010cech Center, Charles University, Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Warsaw, Poland","institution_ids":["https://openalex.org/I108403487"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5075820635"],"corresponding_institution_ids":["https://openalex.org/I108403487","https://openalex.org/I21250087"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.3625,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6616996,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"101","issue":"4","first_page":"827","last_page":"847"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9948999881744385,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9772999882698059,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.8329069018363953},{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.8188908696174622},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7933504581451416},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.6313692331314087},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.6050674915313721},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.511223316192627},{"id":"https://openalex.org/keywords/congruence","display_name":"Congruence (geometry)","score":0.5072824358940125},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45563003420829773},{"id":"https://openalex.org/keywords/principal","display_name":"Principal (computer security)","score":0.4216841459274292},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39157384634017944},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37844228744506836},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3296245336532593},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06506946682929993}],"concepts":[{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.8329069018363953},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.8188908696174622},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7933504581451416},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.6313692331314087},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.6050674915313721},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.511223316192627},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.5072824358940125},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45563003420829773},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.4216841459274292},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39157384634017944},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37844228744506836},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3296245336532593},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06506946682929993},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11225-013-9499-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-013-9499-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-013-9499-y.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"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":"Studia Logica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11225-013-9499-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-013-9499-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-013-9499-y.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"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":"Studia Logica","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.41999998688697815,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320322637","display_name":"Politechnika Warszawska","ror":"https://ror.org/00y0xnp53"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2109908460.pdf","grobid_xml":"https://content.openalex.org/works/W2109908460.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W131260692","https://openalex.org/W278229615","https://openalex.org/W1039618327","https://openalex.org/W1493313128","https://openalex.org/W1554619471","https://openalex.org/W1572222062","https://openalex.org/W2004384679","https://openalex.org/W2011556534","https://openalex.org/W2041835071","https://openalex.org/W2050498524","https://openalex.org/W2054550828","https://openalex.org/W2054891104","https://openalex.org/W2077395144","https://openalex.org/W2084803705","https://openalex.org/W2093865192","https://openalex.org/W2095367681","https://openalex.org/W2116090797","https://openalex.org/W2128124354","https://openalex.org/W2253467077","https://openalex.org/W2482933771","https://openalex.org/W4242462843","https://openalex.org/W4247128566","https://openalex.org/W4247559916","https://openalex.org/W4249714686"],"related_works":["https://openalex.org/W77573719","https://openalex.org/W2385511935","https://openalex.org/W3007066267","https://openalex.org/W2944618814","https://openalex.org/W3134823879","https://openalex.org/W2382432157","https://openalex.org/W4391061523","https://openalex.org/W2801977597","https://openalex.org/W2382598115","https://openalex.org/W2594479762"],"abstract_inverted_index":{"We":[0],"provide":[1],"a":[2,32,63,78],"new":[3],"proof":[4],"of":[5,43,52,86],"the":[6,41,44,50,84],"following":[7],"Pa\u0142asi\u0144ska's":[8],"theorem:":[9],"Every":[10],"finitely":[11,20,100],"generated":[12,101],"protoalgebraic":[13,33,102],"relation":[14,103],"distributive":[15,104],"equality":[16,34,105],"free":[17,35,106],"quasivariety":[18,36],"is":[19,77],"axiomatizable.":[21],"The":[22],"main":[23],"tool":[24,58],"we":[25,61],"use":[26],"are":[27,40],"$${\\mathcal{Q}}$$":[28,37,68,74],"-relation":[29],"formulas":[30,46],"for":[31,48,67,94,99],".":[38],"They":[39],"counterparts":[42],"congruence":[45],"used":[47],"describing":[49],"generation":[51],"congruences":[53],"in":[54,59],"algebras.":[55],"Having":[56],"this":[57],"hand,":[60],"prove":[62],"finite":[64],"axiomatization":[65],"theorem":[66],"when":[69],"it":[70],"has":[71],"definable":[72],"principal":[73,87],"-subrelations.":[75],"This":[76],"property":[79],"obtained":[80],"by":[81,90],"carrying":[82],"over":[83],"definability":[85],"subcongruences,":[88],"invented":[89],"Baker":[91],"and":[92,96],"Wang":[93],"varieties,":[95],"which":[97],"holds":[98],"quasivarieties.":[107]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}