{"id":"https://openalex.org/W1993364664","doi":"https://doi.org/10.2178/jsl/1190150055","title":"How to extend the semantic tableaux and cut-free versions of the second incompleteness theorem almost to Robinson's arithmetic q","display_name":"How to extend the semantic tableaux and cut-free versions of the second incompleteness theorem almost to Robinson's arithmetic q","publication_year":2002,"publication_date":"2002-03-01","ids":{"openalex":"https://openalex.org/W1993364664","doi":"https://doi.org/10.2178/jsl/1190150055","mag":"1993364664"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1190150055","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150055","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/A5074770137","display_name":"Dan E. Willard","orcid":null},"institutions":[{"id":"https://openalex.org/I113508548","display_name":"Albany State University","ror":"https://ror.org/01vme4277","country_code":"US","type":"education","lineage":["https://openalex.org/I113508548"]},{"id":"https://openalex.org/I1327163397","display_name":"State University of New York","ror":"https://ror.org/01q1z8k08","country_code":"US","type":"education","lineage":["https://openalex.org/I1327163397"]},{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dan E. Willard","raw_affiliation_strings":["Computer Science Department, State University of New York, at Albany, Albany, New York 12222, E-mail:","State University of New York ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, State University of New York, at Albany, Albany, New York 12222, E-mail:","institution_ids":["https://openalex.org/I113508548","https://openalex.org/I392282"]},{"raw_affiliation_string":"State University of New York ,","institution_ids":["https://openalex.org/I1327163397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074770137"],"corresponding_institution_ids":["https://openalex.org/I113508548","https://openalex.org/I1327163397","https://openalex.org/I392282"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":3.5191,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.92522425,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"67","issue":"1","first_page":"465","last_page":"496"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9944999814033508,"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":0.9944999814033508,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9898999929428101,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9724000096321106,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/peano-axioms","display_name":"Peano axioms","score":0.7578029632568359},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7094570994377136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6911634206771851},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6026009321212769},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5142138004302979},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.4583664536476135},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.4513194262981415},{"id":"https://openalex.org/keywords/g\u00f6dels-incompleteness-theorems","display_name":"G\u00f6del's incompleteness theorems","score":0.44740229845046997},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14571431279182434},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08172208070755005}],"concepts":[{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.7578029632568359},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7094570994377136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6911634206771851},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6026009321212769},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5142138004302979},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.4583664536476135},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.4513194262981415},{"id":"https://openalex.org/C180937797","wikidata":"https://www.wikidata.org/wiki/Q200787","display_name":"G\u00f6del's incompleteness theorems","level":3,"score":0.44740229845046997},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14571431279182434},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08172208070755005},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C2781302003","wikidata":"https://www.wikidata.org/wiki/Q3294091","display_name":"G\u00f6del","level":2,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1190150055","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150055","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/1190150055","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1190150055","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W969295556","https://openalex.org/W1482532876","https://openalex.org/W1515297838","https://openalex.org/W1515761141","https://openalex.org/W1536217426","https://openalex.org/W1554618854","https://openalex.org/W1572451808","https://openalex.org/W1978270323","https://openalex.org/W1984820433","https://openalex.org/W1985956422","https://openalex.org/W2011612028","https://openalex.org/W2035004935","https://openalex.org/W2035207489","https://openalex.org/W2078123020","https://openalex.org/W2116784727","https://openalex.org/W2169685450","https://openalex.org/W2170622107","https://openalex.org/W2227462403","https://openalex.org/W2492590561","https://openalex.org/W2576543090","https://openalex.org/W3039529476","https://openalex.org/W4233253115","https://openalex.org/W4239934161","https://openalex.org/W4248733413","https://openalex.org/W4298207198","https://openalex.org/W4301968143","https://openalex.org/W6630867569"],"related_works":["https://openalex.org/W2021331155","https://openalex.org/W1572451808","https://openalex.org/W2169685450","https://openalex.org/W2086098666","https://openalex.org/W2035207489","https://openalex.org/W2167493425","https://openalex.org/W2071373355","https://openalex.org/W2071977753","https://openalex.org/W1996215903","https://openalex.org/W1985956422","https://openalex.org/W2011612028","https://openalex.org/W2040404640","https://openalex.org/W2227462403","https://openalex.org/W2036869460","https://openalex.org/W1984820433","https://openalex.org/W1554618854","https://openalex.org/W1515297838","https://openalex.org/W2170622107","https://openalex.org/W2022687341","https://openalex.org/W1997679513"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"us":[2],"recall":[3],"that":[4,13,47,70,126],"Raphael":[5],"Robinson's":[6],"Arithmetic":[7,17],"Q":[8,79],"is":[9,73],"an":[10,151],"axiom":[11,100,109,138],"system":[12,139],"differs":[14],"from":[15],"Peano":[16],"essentially":[18],"by":[19,158],"containing":[20],"no":[21],"Induction":[22],"axioms":[23],"[13],":[24],"[18].":[25],"We":[26,44],"will":[27,45,84,96,123],"generalize":[28],"the":[29,33,39,58,62,117,127,131,137],"semantic-tableaux":[30,128],"version":[31,129],"of":[32,41,61,78,130],"Second":[34,132],"Incompleteness":[35,133],"Theorem":[36,134],"almost":[37],"to":[38,87,99],"level":[40],"System":[42],"Q.":[43],"prove":[46,88],"there":[48],"exists":[49],"a":[50,112],"single":[51],"rather":[52],"long":[53],"\u03a01":[54],"sentence,":[55],"valid":[56],"in":[57],"standard":[59],"model":[60],"Natural":[63],"Numbers":[64],"and":[65,160],"denoted":[66],"as":[67,141,143],"V.":[68],"such":[69],"if":[71],"\u03b1":[72,83,102],"any":[74],"finite":[75],"consistent":[76],"extension":[77],"+":[80],"V":[81],"then":[82],"be":[85],"unable":[86],"its":[89,146],"Semantic":[90],"Tableaux":[91],"consistency.":[92],"The":[93],"same":[94],"result":[95],"also":[97,124],"apply":[98],"systems":[101,110],"with":[103],"infinite":[104],"cardinality":[105],"when":[106],"these":[107],"infinite-sized":[108],"satisfy":[111],"minor":[113],"additional":[114],"constraint,":[115],"called":[116],"Conventional":[118],"Encoding":[119],"Property.":[120],"Our":[121],"formalism":[122],"imply":[125],"generalizes":[135],"for":[136,144],"I\u03a30,":[140],"well":[142],"all":[145],"natural":[147],"extensions.":[148],"(This":[149],"answers":[150],"open":[152],"question":[153],"raised":[154],"twenty":[155],"years":[156],"ago":[157],"Paris":[159],"Wilkie":[161],"[15].)":[162]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
