{"id":"https://openalex.org/W2017704340","doi":"https://doi.org/10.1305/ndjfl/1093893348","title":"Note on definitional reductions.","display_name":"Note on definitional reductions.","publication_year":1968,"publication_date":"1968-01-01","ids":{"openalex":"https://openalex.org/W2017704340","doi":"https://doi.org/10.1305/ndjfl/1093893348","mag":"2017704340"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093893348","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093893348","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-9/issue-1/Note-on-definitional-reductions/10.1305/ndjfl/1093893348.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-9/issue-1/Note-on-definitional-reductions/10.1305/ndjfl/1093893348.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030590840","display_name":"Jonathan P. Seldin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jonathan P. Seldin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030590840"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.16549047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","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":0.979200005531311,"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":0.979200005531311,"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/T11567","display_name":"semigroups and automata theory","score":0.932699978351593,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9136999845504761,"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":0.6990987658500671},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6479461193084717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5413475036621094},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5136527419090271},{"id":"https://openalex.org/keywords/curry","display_name":"Curry","score":0.4326241910457611},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40755975246429443},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.33587461709976196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31614595651626587},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.23503944277763367}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6990987658500671},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6479461193084717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5413475036621094},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5136527419090271},{"id":"https://openalex.org/C2781029818","wikidata":"https://www.wikidata.org/wiki/Q2368856","display_name":"Curry","level":2,"score":0.4326241910457611},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40755975246429443},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.33587461709976196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31614595651626587},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.23503944277763367},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093893348","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093893348","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-9/issue-1/Note-on-definitional-reductions/10.1305/ndjfl/1093893348.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/1093893348","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093893348","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/1093893348","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093893348","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-9/issue-1/Note-on-definitional-reductions/10.1305/ndjfl/1093893348.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":[{"score":0.6299999952316284,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2017704340.pdf","grobid_xml":"https://content.openalex.org/works/W2017704340.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2074025367","https://openalex.org/W4302314483"],"related_works":["https://openalex.org/W4300022558","https://openalex.org/W4243970755","https://openalex.org/W2518544609","https://openalex.org/W2282931459","https://openalex.org/W4247777465","https://openalex.org/W2896691900","https://openalex.org/W2920629453","https://openalex.org/W2520149502","https://openalex.org/W2164890668","https://openalex.org/W1596503157"],"abstract_inverted_index":{"(1)":[0],"XDY&":[1],"\u03a6(Al9":[2],".":[3,4,5,19,20,21,59,60,61],",Am)DZ==>X\u03cbY":[6],"where":[7],"Y":[8,12],"is":[9,34,56,100,110,131],"formed":[10],"from":[11],"by":[13,24],"replacing":[14],"one":[15,66],"occurrence":[16],"of":[17,67,83,97,133,153],"\u03a6{Ah":[18],",":[22,62],"Am)":[23,63],"Z.":[25],"The":[26,50,81,95],"older":[27],"restriction,":[28,52],"used":[29,53],"in":[30,54,92,135],"[CLg]":[31],"and":[32,145],"[DFS]":[33],"that":[35,57,108,117,132],"Z":[36],"be":[37,65],"a":[38],"basic":[39,129,154],"ob.":[40],"I":[41,71,141],"will":[42,72,142],"call":[43,73],"the":[44,68,74,118,136],"rule":[45,75],"with":[46,76],"this":[47,77,98,103],"restriction":[48,79],"Rd":[49],"other":[51],"[FML],":[55],"\u03a6(Ai,":[58],"DZ":[64],"defining":[69],"axioms.":[70],"latter":[78],"Rd*.":[80],"equivalence":[82],"these":[84],"two":[85,119],"rules":[86],"was":[87],"apparently":[88],"taken":[89],"for":[90,123,151],"granted":[91],"Curry's":[93],"work.":[94],"purpose":[96],"note":[99],"to":[101,125,139,149],"verify":[102],"equivalence.":[104],"It":[105],"turns":[106],"out":[107],"Rd*":[109],"slightly":[111],"more":[112],"general":[113],"than":[114],"Rd,":[115],"but":[116],"are":[120],"precisely":[121],"equivalent":[122],"reductions":[124],"ultimate":[126],"definienda.":[127],"My":[128],"notation":[130],"Curry":[134],"papers":[137],"referred":[138],"above.":[140],"use":[143],"'21'":[144],"f":[146],"\u03b4":[147],"'":[148],"stand":[150],"sequences":[152],"obs.":[155]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}