{"id":"https://openalex.org/W2078172531","doi":"https://doi.org/10.1305/ndjfl/1093893855","title":"Final word on a shortest implicational axiom.","display_name":"Final word on a shortest implicational axiom.","publication_year":1970,"publication_date":"1970-01-01","ids":{"openalex":"https://openalex.org/W2078172531","doi":"https://doi.org/10.1305/ndjfl/1093893855","mag":"2078172531"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093893855","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093893855","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-11/issue-1/Final-word-on-a-shortest-implicational-axiom/10.1305/ndjfl/1093893855.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-11/issue-1/Final-word-on-a-shortest-implicational-axiom/10.1305/ndjfl/1093893855.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109366683","display_name":"Ivo Thomas","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ivo Thomas","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109366683"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.22696929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9789999723434448,"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":0.9789999723434448,"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":0.9408000111579895,"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/axiom","display_name":"Axiom","score":0.5924080014228821},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.43246033787727356},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.4282219707965851},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42692068219184875},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32211625576019287},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04031950235366821}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5924080014228821},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.43246033787727356},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.4282219707965851},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42692068219184875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32211625576019287},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04031950235366821}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093893855","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093893855","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-11/issue-1/Final-word-on-a-shortest-implicational-axiom/10.1305/ndjfl/1093893855.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1093893855","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093893855","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1093893855","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093893855","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-11/issue-1/Final-word-on-a-shortest-implicational-axiom/10.1305/ndjfl/1093893855.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2078172531.pdf","grobid_xml":"https://content.openalex.org/works/W2078172531.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1976353188","https://openalex.org/W2084199183","https://openalex.org/W6643983369","https://openalex.org/W6671685062"],"related_works":["https://openalex.org/W2753083100","https://openalex.org/W3198799031","https://openalex.org/W2090831035","https://openalex.org/W1584952351","https://openalex.org/W2081948323","https://openalex.org/W2927058411","https://openalex.org/W3005084276","https://openalex.org/W2156879229","https://openalex.org/W2803105815","https://openalex.org/W3124251996"],"abstract_inverted_index":{"In":[0],"[l]":[1],"it":[2],"is":[3,21,26],"shown":[4],"that":[5],"the":[6,17,30],"only":[7],"other":[8],"candidate":[9],"for":[10],"a":[11],"shortest":[12],"sole":[13],"implicational":[14],"axiom":[15],"besides":[16],"CCCpqrCCrpCsp":[18],"of":[19],"Lukasiewicz":[20],"(1)":[22,25],"CCrpCCCpqrCsp.":[23],"But":[24],"ruled":[27],"out":[28],"by":[29],"matrix":[31]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}