{"id":"https://openalex.org/W2039356064","doi":"https://doi.org/10.2307/2275435","title":"Polynomially and superexponentially shorter proofs in fragments of arithmetic","display_name":"Polynomially and superexponentially shorter proofs in fragments of arithmetic","publication_year":1992,"publication_date":"1992-09-01","ids":{"openalex":"https://openalex.org/W2039356064","doi":"https://doi.org/10.2307/2275435","mag":"2039356064"},"language":"en","primary_location":{"id":"doi:10.2307/2275435","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275435","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/A5109033991","display_name":"Franco Montagna","orcid":null},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Franco Montagna","raw_affiliation_strings":["Scuola di Specializzione in Logica Matematica, Universit\u00e0 di Siena, 53100 Siena, Italy, E-mail:","Universit\u00e0 Di Siena"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Scuola di Specializzione in Logica Matematica, Universit\u00e0 di Siena, 53100 Siena, Italy, E-mail:","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"Universit\u00e0 Di Siena","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109033991"],"corresponding_institution_ids":["https://openalex.org/I102064193"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.17552682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"57","issue":"3","first_page":"844","last_page":"863"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9993000030517578,"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/T11567","display_name":"semigroups and automata theory","score":0.9993000030517578,"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":0.9962999820709229,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9850999712944031,"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/peano-axioms","display_name":"Peano axioms","score":0.7991949319839478},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7161726355552673},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6746090650558472},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5778995156288147},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.529843807220459},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4812321662902832},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.47975954413414},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.4581742286682129},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44539833068847656},{"id":"https://openalex.org/keywords/primitive-recursive-function","display_name":"Primitive recursive function","score":0.42091453075408936},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4051588773727417},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39458590745925903},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36034178733825684},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.32749712467193604},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21359944343566895}],"concepts":[{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.7991949319839478},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7161726355552673},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6746090650558472},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5778995156288147},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.529843807220459},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4812321662902832},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.47975954413414},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.4581742286682129},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44539833068847656},{"id":"https://openalex.org/C9986523","wikidata":"https://www.wikidata.org/wiki/Q1570472","display_name":"Primitive recursive function","level":2,"score":0.42091453075408936},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4051588773727417},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39458590745925903},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36034178733825684},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32749712467193604},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21359944343566895},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2275435","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275435","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/1183744044","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183744044","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":[{"id":"https://metadata.un.org/sdg/4","score":0.7200000286102295,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1975548675","https://openalex.org/W2011612028","https://openalex.org/W2034070758","https://openalex.org/W2040404640","https://openalex.org/W2048735525","https://openalex.org/W2059933820","https://openalex.org/W2106572448","https://openalex.org/W2112754349","https://openalex.org/W2933760589","https://openalex.org/W4206831068","https://openalex.org/W4253934133"],"related_works":["https://openalex.org/W2063064015","https://openalex.org/W2171255643","https://openalex.org/W1616114834","https://openalex.org/W4324296894","https://openalex.org/W2951195380","https://openalex.org/W2122452852","https://openalex.org/W4366809670","https://openalex.org/W1986380412","https://openalex.org/W2064302725","https://openalex.org/W1522616067"],"abstract_inverted_index":{"In":[0,172],"Parikh":[1],"[71]":[2],"it":[3],"is":[4,9,28,63,120,145,180,191,214],"shown":[5],"that,":[6],"if":[7],"T":[8,40,45,59,66,70,75,82,86,132],"an":[10],"r.e.":[11],"consistent":[12],"extension":[13],"of":[14,32,56,80,92,100,165,193,200],"Peano":[15],"arithmetic":[16],"PA":[17,33,93],",":[18,26,94,155],"then,":[19],"for":[20,109],"each":[21],"primitive":[22],"recursive":[23],"function":[24],"g":[25,119,140],"there":[27],"a":[29,54,121,135,151,185,189,201,217],"formula":[30,153],"\u03c6":[31,57,62,101],"such":[34],"that":[35,51,61,130,150,158],"(In":[36],"the":[37,48,78,90,97,105,148],"following,":[38],"Proof":[39,69,81],"(z,":[41,71],"\u03c6)":[42],"and":[43,60,73,84,102,175,182,211],"Prov":[44,74,85,131],"(\u03c6)":[46,87],"denote":[47],"metalinguistic":[49],"assertions":[50],"z":[52],"codes":[53],"proof":[55,138],"in":[58,65,89,163,184],"provable":[64,169,208],"respectively,":[67],"where":[68],"\u250c\u03c6\u2510)":[72],"(\u250c\u03c6\u2510)":[76,133],"are":[77],"formalizations":[79],"(z,\u03c6)":[83],"respectively":[88],"language":[91,204],"\u250c\u03c6\u2510":[95,103],"denotes":[96,104],"G\u00f6del":[98],"number":[99],"corresponding":[106],"numeral.":[107],"Also,":[108],"typographical":[110],"reasons,":[111],"subscripts":[112],"will":[113],"not":[114],"be":[115],"made":[116],"boldface.)":[117],"If":[118],"rapidly":[122],"increasing":[123],"function,":[124],"we":[125],"express":[126],"(1)":[127,159],"by":[128],"saying":[129],"has":[134,167],"much":[136],"shorter":[137],"modulo":[139],"than":[141],"\u03c6.":[142],"Parikh's":[143,212],"result":[144,213],"based":[146],"on":[147],"fact":[149],"suitable":[152,202],"A(x)":[154],"roughly":[156],"asserting":[157],"holds":[160],"with":[161],"x":[162],"place":[164],"\u03c6,":[166],"only":[168,207],"fixed":[170,209],"points.":[171],"de":[173],"Jongh":[174],"Montagna":[176],"[89],":[177],"this":[178],"situation":[179],"generalized":[181],"investigated":[183],"modal":[186,198,203],"context.":[187],"There,":[188],"characterization":[190],"given":[192],"arithmetical":[194],"formulas":[195,199],"arising":[196],"from":[197],"which":[205],"have":[206],"points,":[210],"obtained":[215],"as":[216],"particular":[218],"case.":[219]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
