{"id":"https://openalex.org/W2144488427","doi":"https://doi.org/10.2307/2266613","title":"The elimination theorem when modality is present","display_name":"The elimination theorem when modality is present","publication_year":1952,"publication_date":"1952-12-01","ids":{"openalex":"https://openalex.org/W2144488427","doi":"https://doi.org/10.2307/2266613","mag":"2144488427"},"language":"en","primary_location":{"id":"doi:10.2307/2266613","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2266613","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,"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":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113490577","display_name":"Haskell B. Curry","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Haskell B. Curry","raw_affiliation_strings":["The Pennsylvania State College"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Pennsylvania State College","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5113490577"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.2565445,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"17","issue":"4","first_page":"249","last_page":"265"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9010000228881836,"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/T10142","display_name":"Formal Methods in Verification","score":0.9010000228881836,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.6412361264228821},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5909940600395203},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.5872634053230286},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.560703456401825},{"id":"https://openalex.org/keywords/modality","display_name":"Modality (human\u2013computer interaction)","score":0.49858903884887695},{"id":"https://openalex.org/keywords/section","display_name":"Section (typography)","score":0.41838520765304565},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3876686096191406},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3763227164745331},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33825644850730896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2114395797252655},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05913802981376648},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.05348125100135803},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.05057421326637268}],"concepts":[{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.6412361264228821},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5909940600395203},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.5872634053230286},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.560703456401825},{"id":"https://openalex.org/C2780226545","wikidata":"https://www.wikidata.org/wiki/Q6888030","display_name":"Modality (human\u2013computer interaction)","level":2,"score":0.49858903884887695},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.41838520765304565},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3876686096191406},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3763227164745331},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33825644850730896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2114395797252655},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05913802981376648},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.05348125100135803},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.05057421326637268},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2266613","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2266613","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,"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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183731482","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183731482","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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1528534845","https://openalex.org/W2048288856","https://openalex.org/W2057570323","https://openalex.org/W4238292764"],"related_works":["https://openalex.org/W2560853036","https://openalex.org/W2566696415","https://openalex.org/W1563787543","https://openalex.org/W4239980664","https://openalex.org/W4249026152","https://openalex.org/W4231213805","https://openalex.org/W4244585678","https://openalex.org/W2909241626","https://openalex.org/W2890304493","https://openalex.org/W627697492"],"abstract_inverted_index":{"The":[0,29,133],"present":[1,146],"paper":[2],"contains":[3],"an":[4,97],"emendation":[5],"to":[6,43,67,83,136,140,166],"the":[7,18,24,38,44,69,86,104,117,122,131,154,160,163,167,175],"theory":[8],"of":[9,20,26,31,46,121,152,162,170],"formal":[10],"deducibility":[11],"which":[12,41],"was":[13,58,64],"presented":[14,79],"in":[15,23,34,72,96,108,111,153],"lectures":[16,36],"at":[17,174],"University":[19],"Notre":[21],"Dame":[22],"spring":[25],"1948":[27],"[4].":[28],"method":[30],"proof":[32,71,77,94,139],"developed":[33],"these":[35],"for":[37,127],"elimination":[39,87,123,164],"theorem,":[40],"corresponds":[42],"\u201cHauptsatz\u201d":[45],"Gentzen's":[47],"thesis":[48],"[6],":[49],"failed":[50],"when":[51],"modal":[52,143],"connectives":[53],"were":[54],"present.":[55],"This":[56,75],"deficiency":[57],"remedied":[59],"soon":[60],"thereafter;":[61],"but":[62],"it":[63,113],"not":[65],"possible":[66],"include":[68],"new":[70,76],"those":[73],"lectures.":[74],"is":[78,114,172],"below.":[80],"Before":[81],"proceeding":[82],"this":[84,138],"proof,":[85],"theorem":[88,124,165],"will":[89,147],"be":[90,149],"formulated,":[91],"and":[92],"its":[93],"outlined,":[95],"abstract":[98],"form.":[99],"Certain":[100],"general":[101],"conditions":[102],"on":[103,159],"rules":[105,129,144],"are":[106,145],"formulated":[107],"\u00a71;":[109],"then,":[110],"\u00a72,":[112],"shown":[115],"that":[116],"first":[118],"two":[119],"stages":[120],"go":[125],"through":[126],"any":[128],"satisfying":[130],"conditions.":[132],"modifications":[134],"necessary":[135],"extend":[137],"cases":[141],"where":[142],"then":[148],"taken":[150],"care":[151],"later":[155],"sections.":[156],"A":[157],"section":[158],"extension":[161],"singular":[168],"form":[169],"LC":[171],"added":[173],"end.":[176]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}