{"id":"https://openalex.org/W2068893742","doi":"https://doi.org/10.2307/2275813","title":"A recursive nonstandard model of normal open induction","display_name":"A recursive nonstandard model of normal open induction","publication_year":1996,"publication_date":"1996-12-01","ids":{"openalex":"https://openalex.org/W2068893742","doi":"https://doi.org/10.2307/2275813","mag":"2068893742"},"language":"en","primary_location":{"id":"doi:10.2307/2275813","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275813","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/A5065871959","display_name":"Alessandro Berarducci","orcid":"https://orcid.org/0000-0002-9927-1147"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Alessandro Berarducci","raw_affiliation_strings":["Universit\u00e1 di Pisa, Dipartamento Matematica, Via Buonarroti 2, 56127 Pisa, Italy, E-mail:","Universit\u00e0 di Pisa,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e1 di Pisa, Dipartamento Matematica, Via Buonarroti 2, 56127 Pisa, Italy, E-mail:","institution_ids":["https://openalex.org/I108290504"]},{"raw_affiliation_string":"Universit\u00e0 di Pisa,","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021974011","display_name":"Margarita Otero","orcid":"https://orcid.org/0000-0002-3389-6822"},"institutions":[{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Margarita Otero","raw_affiliation_strings":["Universidad Aut\u00f3noma de Madrid, Departamento Matem\u00e1ticas, Ciudad Universidad de Canto Blanco, 28049 Madrid, Spain, E-mail:","#R##N#Universidad Aut\u00f3noma de Madrid"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad Aut\u00f3noma de Madrid, Departamento Matem\u00e1ticas, Ciudad Universidad de Canto Blanco, 28049 Madrid, Spain, E-mail:","institution_ids":["https://openalex.org/I63634437"]},{"raw_affiliation_string":"#R##N#Universidad Aut\u00f3noma de Madrid","institution_ids":["https://openalex.org/I63634437"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065871959"],"corresponding_institution_ids":["https://openalex.org/I108290504"],"apc_list":null,"apc_paid":null,"fwci":1.1,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.75387833,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"61","issue":"4","first_page":"1228","last_page":"1241"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9812999963760376,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9664000272750854,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.8369590044021606},{"id":"https://openalex.org/keywords/integrally-closed","display_name":"Integrally closed","score":0.6881711483001709},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6801734566688538},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6718453168869019},{"id":"https://openalex.org/keywords/open-set","display_name":"Open set","score":0.6012799143791199},{"id":"https://openalex.org/keywords/mathematical-induction","display_name":"Mathematical induction","score":0.5255776047706604},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5243183374404907},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5123792886734009},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4496751129627228},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3334975242614746},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32783347368240356},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19284319877624512},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18036213517189026},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09736508131027222}],"concepts":[{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.8369590044021606},{"id":"https://openalex.org/C205059728","wikidata":"https://www.wikidata.org/wiki/Q6042740","display_name":"Integrally closed","level":2,"score":0.6881711483001709},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6801734566688538},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6718453168869019},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.6012799143791199},{"id":"https://openalex.org/C206743973","wikidata":"https://www.wikidata.org/wiki/Q178377","display_name":"Mathematical induction","level":2,"score":0.5255776047706604},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5243183374404907},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5123792886734009},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4496751129627228},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3334975242614746},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32783347368240356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19284319877624512},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18036213517189026},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09736508131027222},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2275813","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275813","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/1183745132","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745132","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"},{"id":"pmh:oai:arpi.unipi.it:11568/54852","is_oa":false,"landing_page_url":"http://hdl.handle.net/11568/54852","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1022561181","https://openalex.org/W1965416269","https://openalex.org/W1976479433","https://openalex.org/W1982001540","https://openalex.org/W2059160573","https://openalex.org/W2099293911","https://openalex.org/W2123665570","https://openalex.org/W2201799275","https://openalex.org/W2798442789","https://openalex.org/W4235178139","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4323354904","https://openalex.org/W2993442435","https://openalex.org/W2375826828","https://openalex.org/W4255069280","https://openalex.org/W2143088892","https://openalex.org/W1965300620","https://openalex.org/W2352753919","https://openalex.org/W3215510974","https://openalex.org/W2229776764","https://openalex.org/W4286851433"],"abstract_inverted_index":{"Abstract":[0],"Models":[1],"of":[2,24,44,69,77],"normal":[3,8,28,51,70],"open":[4,19,45,71],"induction":[5,72],"are":[6],"those":[7],"discretely":[9],"ordered":[10,25],"rings":[11],"whose":[12],"nonnegative":[13],"part":[14],"satisfy":[15],"Peano's":[16],"axioms":[17],"for":[18],"formulas":[20],"in":[21,32],"the":[22],"language":[23],"semirings.":[26],"(Where":[27],"means":[29],"integrally":[30],"closed":[31],"its":[33],"fraction":[34],"field.)":[35],"In":[36,60],"1964":[37],"Shepherdson":[38],"gave":[39],"a":[40,65],"recursive":[41,66],"nonstandard":[42,67],"model":[43,48,68],"induction.":[46],"His":[47],"is":[49],"not":[50,54],"and":[52],"does":[53],"have":[55],"any":[56],"infinite":[57,78],"prime":[58,79],"elements.":[59,80],"this":[61],"paper":[62],"we":[63],"present":[64],"with":[73],"an":[74],"unbounded":[75],"set":[76]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}