{"id":"https://openalex.org/W2571623459","doi":"https://doi.org/10.1017/s1755020315000337","title":"FROM STENIUS\u2019 CONSISTENCY PROOF TO SCH\u00dcTTE\u2019S CUT ELIMINATION FOR <i>\u03c9</i>-ARITHMETIC","display_name":"FROM STENIUS\u2019 CONSISTENCY PROOF TO SCH\u00dcTTE\u2019S CUT ELIMINATION FOR <i>\u03c9</i>-ARITHMETIC","publication_year":2015,"publication_date":"2015-12-22","ids":{"openalex":"https://openalex.org/W2571623459","doi":"https://doi.org/10.1017/s1755020315000337","mag":"2571623459"},"language":"en","primary_location":{"id":"doi:10.1017/s1755020315000337","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020315000337","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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":"The Review of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10138/229275","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111576392","display_name":"Annika Siders","orcid":null},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"ANNIKA SIDERS","raw_affiliation_strings":["University of Helsinki"],"affiliations":[{"raw_affiliation_string":"University of Helsinki","institution_ids":["https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111576392"],"corresponding_institution_ids":["https://openalex.org/I133731052"],"apc_list":null,"apc_paid":null,"fwci":0.4314,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.79642072,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"9","issue":"1","first_page":"1","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9921000003814697,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9919999837875366,"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/reduction","display_name":"Reduction (mathematics)","score":0.570448637008667},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.5494225025177002},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5310360193252563},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.505331814289093},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4769769608974457},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.43719688057899475},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.42691272497177124},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.42011696100234985},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40198764204978943},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3796919286251068},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3793449401855469},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2662108540534973},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12696337699890137}],"concepts":[{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.570448637008667},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.5494225025177002},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5310360193252563},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.505331814289093},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4769769608974457},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.43719688057899475},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.42691272497177124},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.42011696100234985},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40198764204978943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3796919286251068},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3793449401855469},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2662108540534973},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12696337699890137},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s1755020315000337","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020315000337","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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":"The Review of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:helda.helsinki.fi:10138/229275","is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/229275","pdf_url":"http://hdl.handle.net/10138/229275","source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:helda.helsinki.fi:10138/229275","is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/229275","pdf_url":"http://hdl.handle.net/10138/229275","source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2571623459.pdf","grobid_xml":"https://content.openalex.org/works/W2571623459.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W132036571","https://openalex.org/W863105744","https://openalex.org/W1528233644","https://openalex.org/W1970743109","https://openalex.org/W2014377715","https://openalex.org/W2039977878","https://openalex.org/W2090663022","https://openalex.org/W2131181713","https://openalex.org/W2318443385","https://openalex.org/W2343121769","https://openalex.org/W3190570980","https://openalex.org/W4238292764"],"related_works":["https://openalex.org/W2257471395","https://openalex.org/W2064351239","https://openalex.org/W1897561465","https://openalex.org/W1966954916","https://openalex.org/W1490568884","https://openalex.org/W2105688121","https://openalex.org/W2093872989","https://openalex.org/W2270389684","https://openalex.org/W1780530600","https://openalex.org/W1485868496"],"abstract_inverted_index":{"Abstract":[0],"The":[1,197],"book":[2],"Das":[3],"Interpretationsproblem":[4],"der":[5],"Formalisierten":[6],"Zahlentheorie":[7],"und":[8],"ihre":[9],"Formale":[10],"Widerspruchsfreiheit":[11],"by":[12,69,82,91,136,206,213],"Erik":[13],"Stenius":[14,56,135],"published":[15],"in":[16,41,63,93,103,139,164,171,240],"1952":[17,153],"contains":[18],"a":[19,28,45,64,107,143,161,172],"consistency":[20],"proof":[21,126,173,227,242],"for":[22,85,109,204],"infinite":[23],"\u03c9":[24,86],"-arithmetic":[25,87],"based":[26,112,189],"on":[27,52,113,148,190],"semantical":[29],"interpretation.":[30],"Despite":[31],"the":[32,37,59,70,73,100,116,122,149,168,215,219,233,248,251],"proof\u2019s":[33],"reference":[34],"to":[35,44,209,256],"semantics":[36,211],"truth":[38],"definition":[39],"is":[40],"fact":[42],"equivalent":[43],"syntactical":[46],"derivability":[47],"or":[48],"reduction":[49,54,102,234,255],"condition.":[50],"Based":[51],"this":[53,96,120,177],"condition":[55],"proves":[57],"that":[58],"complexity":[60,71],"of":[61,72,115,124,151,186,193,218,232,235,247,254],"formulas":[62],"derivation":[65],"can":[66,78],"be":[67,80],"limited":[68],"conclusion.":[74],"This":[75,129],"independent":[76],"result":[77,199],"also":[79],"proved":[81],"cut":[83,110,225,237],"elimination":[84,111,226],"which":[88,239],"was":[89,131],"done":[90],"Sch\u00fctte":[92],"1951.":[94],"In":[95,176],"paper":[97,178],"we":[98,179],"interpret":[99],"syntactic":[101],"Stenius\u2019":[104,125,165,187,210,230],"work":[105],"as":[106,183],"method":[108,170],"invertibility":[114],"logical":[117],"rules.":[118],"Through":[119],"interpretation":[121],"constructivity":[123],"becomes":[127],"apparent.":[128],"improvement":[130,205],"explicitly":[132],"requested":[133],"from":[134,145],"Paul":[137],"Bernays":[138,146,194],"private":[140],"correspondence":[141],"(In":[142],"letter":[144],"begun":[147],"19th":[150],"September":[152],"(Stenius":[154],"&amp;":[155],"Bernays,":[156,158],"1951\u201375)).":[157],"who":[159],"took":[160],"deep":[162],"interest":[163],"manuscript,":[166],"applied":[167],"described":[169],"Herbrand\u2019s":[174,181],"theorem.":[175],"prove":[180],"theorem,":[182],"an":[184],"application":[185],"work,":[188],"lecture":[191],"notes":[192],"(Bernays,":[195],"1961).":[196],"main":[198],"completely":[200],"resolves":[201],"Bernays\u2019":[202],"suggestions":[203],"eliminating":[207],"references":[208],"and":[212,245],"showing":[214],"constructive":[216],"nature":[217],"proof.":[220],"A":[221],"comparison":[222],"with":[223],"Sch\u00fctte\u2019s":[224,241],"shows":[228],"how":[229],"simplification":[231],"universal":[236],"formulas,":[238],"requires":[243],"duplication":[244],"repositioning":[246],"cuts,":[249],"shifts":[250],"problematic":[252],"case":[253],"implications.":[257]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2017-01-26T00:00:00"}
