{"id":"https://openalex.org/W2137023255","doi":"https://doi.org/10.2178/jsl/1286198143","title":"Formalizing non-standard arguments in second-order arithmetic","display_name":"Formalizing non-standard arguments in second-order arithmetic","publication_year":2010,"publication_date":"2010-10-04","ids":{"openalex":"https://openalex.org/W2137023255","doi":"https://doi.org/10.2178/jsl/1286198143","mag":"2137023255"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1286198143","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1286198143","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":"The 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/A5034226803","display_name":"Keita Yokoyama","orcid":"https://orcid.org/0000-0001-5329-3298"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Keita Yokoyama","raw_affiliation_strings":["Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan. E-mail:","Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan. E-mail: y-keita@math.tohoku.ac.jp"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan. E-mail:","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan. E-mail: y-keita@math.tohoku.ac.jp","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034226803"],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":null,"apc_paid":null,"fwci":1.6914,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.84845611,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"75","issue":"4","first_page":"1199","last_page":"1210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"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":0.9973000288009644,"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":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.8680554628372192},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.7294098138809204},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5080361366271973},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4817042946815491},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4689461886882782},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.330472469329834},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3264918327331543},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1468639075756073}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8680554628372192},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7294098138809204},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5080361366271973},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4817042946815491},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4689461886882782},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.330472469329834},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3264918327331543},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1468639075756073},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1286198143","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1286198143","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":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1286198143","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1286198143","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":10,"referenced_works":["https://openalex.org/W1556453281","https://openalex.org/W1572451808","https://openalex.org/W1601654835","https://openalex.org/W2025876280","https://openalex.org/W2038627458","https://openalex.org/W2085905338","https://openalex.org/W2087429103","https://openalex.org/W2094306267","https://openalex.org/W2134310526","https://openalex.org/W4251070772"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W4387820098","https://openalex.org/W1996614773","https://openalex.org/W2576399385","https://openalex.org/W2963408011","https://openalex.org/W4236324517","https://openalex.org/W2184046398"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,19,33],"introduce":[5],"the":[6],"systems":[7],"ns-ACA":[8,41],"0":[9,12,26,29,42,45,50,53],"and":[10,27],"ns-WKL":[11,44],"of":[13],"non-standard":[14,22,38],"second-order":[15],"arithmetic":[16],"in":[17,24,40,48],"which":[18],"can":[20],"formalize":[21],"arguments":[23],"ACA":[25,49],"WKL":[28,52],",":[30],"respectively.":[31],"Then,":[32],"give":[34],"direct":[35],"transformations":[36],"from":[37],"proofs":[39,47],"or":[43,51],"into":[46],".":[54]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
