{"id":"https://openalex.org/W7114909892","doi":"https://doi.org/10.1017/jsl.2026.10255","title":"FINITE AXIOMATIZATION OF Grz \u00d7 S 5 $\\mathbf {Grz}\\times \\mathbf {S5}$ bold upper G r z times bold upper S Baseline bold 5 AND GL \u00d7 S 5 $\\mathbf {GL}\\times \\mathbf {S5}$ bold upper G upper L times bold upper S Baseline bold 5","display_name":"FINITE AXIOMATIZATION OF Grz \u00d7 S 5 $\\mathbf {Grz}\\times \\mathbf {S5}$ bold upper G r z times bold upper S Baseline bold 5 AND GL \u00d7 S 5 $\\mathbf {GL}\\times \\mathbf {S5}$ bold upper G upper L times bold upper S Baseline bold 5","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7114909892","doi":"https://doi.org/10.1017/jsl.2026.10255"},"language":"en","primary_location":{"id":"doi:10.1017/jsl.2026.10255","doi":"https://doi.org/10.1017/jsl.2026.10255","is_oa":false,"landing_page_url":"https://doi.org/10.1017/jsl.2026.10255","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","ccf-c","cwts-core","dongbi-c","erih-plus","jufo-2","norway-2","poland-200","russia-white-list-2"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2512.09381","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"GURAM BEZHANISHVILI","orcid":"https://orcid.org/0009-0008-9721-246X","observed_orcids":["https://orcid.org/0009-0008-9721-246X"]},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"GURAM BEZHANISHVILI","raw_affiliation_strings":["NEW MEXICO STATE UNIVERSITY"],"raw_orcid":"https://orcid.org/0009-0008-9721-246X","affiliations":[{"raw_affiliation_string":"NEW MEXICO STATE UNIVERSITY","institution_ids":["https://openalex.org/I10052268"]}]},{"author_position":"last","author":{"id":null,"display_name":"MASHIATH KHAN","orcid":"https://orcid.org/0009-0004-9108-5392","observed_orcids":["https://orcid.org/0009-0004-9108-5392"]},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"MASHIATH KHAN","raw_affiliation_strings":["NEW MEXICO STATE UNIVERSITY"],"raw_orcid":"https://orcid.org/0009-0004-9108-5392","affiliations":[{"raw_affiliation_string":"NEW MEXICO STATE UNIVERSITY","institution_ids":["https://openalex.org/I10052268"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I10052268"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04317738,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.6840999722480774,"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":0.6840999722480774,"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":0.28760001063346863,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.014399999752640724,"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/finite-axiomatizability","display_name":"finite axiomatizability","score":0.9039999842643738},{"id":"https://openalex.org/keywords/product-logic","display_name":"product logic","score":0.531000018119812},{"id":"https://openalex.org/keywords/product-matching","display_name":"product matching","score":0.7009999752044678},{"id":"https://openalex.org/keywords/modal-logic","display_name":"modal logic","score":0.6790000200271606}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5051000118255615},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.4830999970436096},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.47749999165534973},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.3873000144958496},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C98224912","wikidata":"https://www.wikidata.org/wiki/Q6901647","display_name":"Monoidal t-norm logic","level":5,"score":0.34950000047683716},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3443000018596649},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.32499998807907104},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.32249999046325684},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3199000060558319},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3012999892234802},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27649998664855957}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/jsl.2026.10255","doi":"https://doi.org/10.1017/jsl.2026.10255","is_oa":false,"landing_page_url":"https://doi.org/10.1017/jsl.2026.10255","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","ccf-c","cwts-core","dongbi-c","erih-plus","jufo-2","norway-2","poland-200","russia-white-list-2"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2512.09381","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.09381","pdf_url":"https://arxiv.org/pdf/2512.09381","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":"doi:10.48550/arxiv.2512.09381","doi":"https://doi.org/10.48550/arxiv.2512.09381","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.09381","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2512.09381","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.09381","pdf_url":"https://arxiv.org/pdf/2512.09381","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7114909892.pdf","grobid_xml":"https://content.openalex.org/works/W7114909892.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2085722670","https://openalex.org/W1487533219","https://openalex.org/W4414987646","https://openalex.org/W4243110573","https://openalex.org/W7095198755","https://openalex.org/W4391383761","https://openalex.org/W4287755661","https://openalex.org/W3004134876","https://openalex.org/W4405468612","https://openalex.org/W1878021248"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"develop":[2],"a":[3,29],"selective":[4],"filtration":[5],"technique":[6],"for":[7,128],"the":[8,15,24,86,113,117,123,131,146,150,157,165,168],"monadic":[9,16,118],"Grzegorczyk":[10,152],"and":[11,58,153],"G\u00f6del\u2013L\u00f6b":[12,154],"logics":[13,22,133,155],"with":[14,156],"Barcan":[17,158],"formula,":[18],"yielding":[19],"that":[20,33,59,145],"these":[21],"have":[23],"finite":[25,126],"model":[26],"property.":[27],"As":[28,140],"consequence,":[30,142],"we":[31,143],"obtain":[32,144],"GL":[34],"\u00d7":[35,61],"S":[36,51,62,77,91,107],"5":[37,54,63,80,92,110],"$\\mathbf":[38,64],"{GL}":[39],"\\times":[40,66],"\\mathbf":[41,67],"{S5}$":[42,68],"bold":[43,49,53,69,75,79,99,105,109],"upper":[44,46,50,70,76,100,106],"G":[45,71,101],"L":[47],"times":[48,74],"Baseline":[52,78,108],"is":[55,81],"product":[56,132],"matching,":[57],"Grz":[60,89],"{Grz}":[65],"r":[72,102],"z":[73,103],"axiomatized":[82],"by":[83],"adding":[84],"to":[85],"commutator":[87],"[":[88],",":[90],"]":[93],"$[\\mathbf":[94],"{Grz},\\mathbf":[95],"{S5}]$":[96],"left":[97],"bracket":[98,112],"comma":[104],"right":[111],"G\u00f6del":[114],"translation":[115],"of":[116,125,130,149,167],"Casari":[119],"formula.":[120],"This":[121],"settles":[122],"question":[124],"axiomatization":[127],"two":[129],"listed":[134],"in":[135],"[13,":[136],"p.":[137],"137]":[138],".":[139],"another":[141],"one-variable":[147],"fragments":[148],"predicate":[151,170],"formula":[159],"are":[160],"Kripke":[161],"complete":[162],"(which":[163],"contrasts":[164],"incompleteness":[166],"full":[169],"logics).":[171]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2025-12-12T00:00:00"}