{"id":"https://openalex.org/W2074997100","doi":"https://doi.org/10.2307/2272168","title":"An interpolation lemma for the pure implicational calculus","display_name":"An interpolation lemma for the pure implicational calculus","publication_year":1975,"publication_date":"1975-09-01","ids":{"openalex":"https://openalex.org/W2074997100","doi":"https://doi.org/10.2307/2272168","mag":"2074997100"},"language":"en","primary_location":{"id":"doi:10.2307/2272168","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2272168","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/A5083853769","display_name":"Roy Edelstein","orcid":null},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Roy Edelstein","raw_affiliation_strings":["Ohio State University, Columbus, Ohio 43210","Ohio State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ohio State University, Columbus, Ohio 43210","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"Ohio State University","institution_ids":["https://openalex.org/I52357470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5083853769"],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.1517155,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"3","first_page":"443","last_page":"444"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9467999935150146,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9467999935150146,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.928600013256073,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9240999817848206,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/lemma","display_name":"Lemma (botany)","score":0.9104127287864685},{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.6934642195701599},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.657367467880249},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5597288608551025},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5341706871986389},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.5005977153778076},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4955703020095825},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.439573734998703},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37951916456222534},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36388683319091797},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3575083911418915},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1368715763092041},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.09212222695350647},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.059306710958480835},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.04984351992607117},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.04925769567489624}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.9104127287864685},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.6934642195701599},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.657367467880249},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5597288608551025},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5341706871986389},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.5005977153778076},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4955703020095825},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.439573734998703},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37951916456222534},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36388683319091797},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3575083911418915},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1368715763092041},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.09212222695350647},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.059306710958480835},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.04984351992607117},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.04925769567489624},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2272168","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2272168","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/1183739476","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183739476","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2059922809","https://openalex.org/W2387527986","https://openalex.org/W2479250593","https://openalex.org/W2808944898","https://openalex.org/W4283261428","https://openalex.org/W2131148043","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W1998171255","https://openalex.org/W4221036368"],"abstract_inverted_index":{"Although":[0],"a":[1,113],"variety":[2],"of":[3,19,44,84,95],"proofs":[4],"are":[5,26],"available":[6],"for":[7,70],"the":[8,22,51,55,82,93,138],"Craig-Lyndon":[9],"Interpolation":[10,52,86],"Lemma,":[11],"they":[12,25],"all":[13],"seem":[14],"to":[15,28,54,99],"make":[16],"essential":[17],"use":[18,43],"negation,":[20],"with":[21],"result":[23],"that":[24,41,124],"inapplicable":[27],"deductive":[29],"theories":[30],"in":[31,76,121,161,166],"which":[32],"negation":[33,45],"cannot":[34],"be":[35,47,92],"expressed.":[36],"It":[37],"is":[38,107,112,151],"here":[39],"shown":[40],"this":[42],"can":[46],"avoided":[48],"by":[49,137,152],"extending":[50],"Lemma":[53,87,141],"pure":[56],"implicational":[57],"calculus":[58],"PCI.":[59,89],"Determinate":[60,139],"Parameter":[61,140],"Lemma.":[62],"For":[63,88],"each":[64],"formula":[65,114],"A,":[66],"\u22a8PA":[67,134,146],"\u2283":[68,104,126,130,135,144,147],"A":[69,100,136],"some":[71],"sentence":[72,96,118],"parameter":[73,119],"PA":[74,158,169],"occurring":[75],"A.":[77,85,167],"Proof.":[78,132],"By":[79],"induction":[80],"on":[81],"construction":[83],"Let":[90],"\u0393":[91],"set":[94],"parameters":[97],"common":[98],"and":[101,105,128,142],"C.If":[102],"\u22a8A":[103,125,143],"C":[106,150,162],"not":[108,120],"valid,":[109],"then":[110],"there":[111],"B":[115,127],"containing":[116],"no":[117],"Y":[122],"such":[123],"\u22a8B":[129],"C.":[131,148],"Since":[133],"C,":[145],"But":[149],"hypothesis":[153],"an":[154],"invalid":[155],"formula,":[156],"so":[157],"must":[159],"occur":[160],"as":[163,165],"well":[164],"Thus":[168],"\u0404":[170],"\u0393.":[171]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
