{"id":"https://openalex.org/W1986737842","doi":"https://doi.org/10.2307/2275677","title":"On external Scott algebras in nonstandard models of Peano arithmetic","display_name":"On external Scott algebras in nonstandard models of Peano arithmetic","publication_year":1996,"publication_date":"1996-06-01","ids":{"openalex":"https://openalex.org/W1986737842","doi":"https://doi.org/10.2307/2275677","mag":"1986737842"},"language":"en","primary_location":{"id":"doi:10.2307/2275677","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275677","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/A5087847817","display_name":"Vladimir Kanovei","orcid":"https://orcid.org/0000-0001-7415-9784"},"institutions":[{"id":"https://openalex.org/I134694890","display_name":"Russian University of Transport","ror":"https://ror.org/05gba0366","country_code":"RU","type":"education","lineage":["https://openalex.org/I134694890"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Vladimir Kanovei","raw_affiliation_strings":["Department of Mathematics (Vychislitelnaya), Moscow Transport Engineering Institute, Obraztsova 15, Moscow 101475, Russia, E-mail:","Moscow Transport Engineering Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics (Vychislitelnaya), Moscow Transport Engineering Institute, Obraztsova 15, Moscow 101475, Russia, E-mail:","institution_ids":["https://openalex.org/I134694890"]},{"raw_affiliation_string":"Moscow Transport Engineering Institute","institution_ids":["https://openalex.org/I134694890"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5087847817"],"corresponding_institution_ids":["https://openalex.org/I134694890"],"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":0.1179941,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"61","issue":"2","first_page":"586","last_page":"607"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9962999820709229,"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":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.9640095233917236},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.8496677875518799},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8381118774414062},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.7939581274986267},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.6063170433044434},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.5903023481369019},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.47474056482315063},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4728667438030243},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.46086108684539795},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.437957763671875},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41501298546791077},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3462323248386383},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07322618365287781}],"concepts":[{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.9640095233917236},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.8496677875518799},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8381118774414062},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.7939581274986267},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.6063170433044434},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.5903023481369019},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.47474056482315063},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4728667438030243},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.46086108684539795},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.437957763671875},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41501298546791077},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3462323248386383},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07322618365287781},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2275677","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275677","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/1183745016","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745016","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":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W83139932","https://openalex.org/W1566235828","https://openalex.org/W1601654835","https://openalex.org/W2169463915","https://openalex.org/W4231202900"],"related_works":["https://openalex.org/W1543500847","https://openalex.org/W87599178","https://openalex.org/W2017398442","https://openalex.org/W1991956515","https://openalex.org/W4206411991","https://openalex.org/W2023423328","https://openalex.org/W2059028119","https://openalex.org/W2003918494","https://openalex.org/W1616114834","https://openalex.org/W2063064015"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"prove":[2],"that":[3],"a":[4,10,30,37],"necessary":[5],"and":[6,63],"sufficient":[7],"condition":[8],"for":[9],"countable":[11],"set":[12,67],"of":[13,15,23,26,34,39,68,81,83,88],"sets":[14,25,82],"integers":[16,27,84],"to":[17,20,79],"be":[18],"equal":[19],"the":[21,40,46,66],"algebra":[22],"all":[24,69],"definable":[28],"in":[29,85],"nonstandard":[31,53],"elementary":[32,86],"extension":[33],"\u03c9":[35,89],"by":[36],"formula":[38],"PA":[41],"language":[42],"which":[43],"may":[44],"include":[45],"standardness":[47],"predicate":[48],"but":[49],"does":[50],"not":[51],"contain":[52],"parameters,":[54],"is":[55,58],"as":[56],"follows:":[57],"closed":[59],"under":[60],"arithmetical":[61,74],"definability":[62,80],"contains":[64],"0(\u03c9)":[65],"(G\u00f6del":[70],"numbers":[71],"of)":[72],"true":[73],"sentences.":[75],"Some":[76],"results":[77],"related":[78],"extensions":[87],"are":[90],"included.":[91]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}