{"id":"https://openalex.org/W2079718016","doi":"https://doi.org/10.2307/2586587","title":"Models of arithmetic and subuniform bounds for the arithmetic sets","display_name":"Models of arithmetic and subuniform bounds for the arithmetic sets","publication_year":1998,"publication_date":"1998-03-01","ids":{"openalex":"https://openalex.org/W2079718016","doi":"https://doi.org/10.2307/2586587","mag":"2079718016"},"language":"en","primary_location":{"id":"doi:10.2307/2586587","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586587","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/A5045989401","display_name":"A. H. Lachlan","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Alistair H. Lachlan","raw_affiliation_strings":["Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, CanadaV5A 1S6, E-mail:","Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6, E-mail: alistair@sfu.ca"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, CanadaV5A 1S6, E-mail:","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6, E-mail: alistair@sfu.ca","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023422267","display_name":"Robert I. Soare","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert I. Soare","raw_affiliation_strings":["Department of Mathematics, University of Chicago, Chicago, Illinois 60637-1546, USA, E-mail:","Department of Mathematics, University of Chicago, Chicago, Illinois 60637-1546, USA, E-mail: soare@math.uchicago.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Chicago, Chicago, Illinois 60637-1546, USA, E-mail:","institution_ids":["https://openalex.org/I40347166","https://openalex.org/I39422238"]},{"raw_affiliation_string":"Department of Mathematics, University of Chicago, Chicago, Illinois 60637-1546, USA, E-mail: soare@math.uchicago.edu","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.21063163,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"63","issue":"1","first_page":"59","last_page":"72"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9686999917030334,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9686999917030334,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9570000171661377,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9462000131607056,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/arithmetic","display_name":"Arithmetic","score":0.7963337898254395},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7452644109725952},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7045390605926514},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.6941463947296143},{"id":"https://openalex.org/keywords/arithmetic-circuit-complexity","display_name":"Arithmetic circuit complexity","score":0.6308326125144958},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.6042931079864502},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.5203073024749756},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.44307321310043335},{"id":"https://openalex.org/keywords/arithmetic-progression","display_name":"Arithmetic progression","score":0.43992874026298523},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36567169427871704},{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.055655449628829956}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7963337898254395},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7452644109725952},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7045390605926514},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.6941463947296143},{"id":"https://openalex.org/C155920423","wikidata":"https://www.wikidata.org/wiki/Q4791120","display_name":"Arithmetic circuit complexity","level":3,"score":0.6308326125144958},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.6042931079864502},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.5203073024749756},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.44307321310043335},{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.43992874026298523},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36567169427871704},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.055655449628829956},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2307/2586587","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586587","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/1183745457","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745457","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:CiteSeerX.psu:10.1.1.46.9585","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.9585","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uchicago.edu/~soare/papers/suub.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.54.346","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.346","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cs.uchicago.edu/pub/users/soare/suub.ps","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":8,"referenced_works":["https://openalex.org/W169333546","https://openalex.org/W1511682313","https://openalex.org/W1995739498","https://openalex.org/W2034579698","https://openalex.org/W2048019510","https://openalex.org/W2060075008","https://openalex.org/W2078971842","https://openalex.org/W4231202900"],"related_works":["https://openalex.org/W2181927644","https://openalex.org/W2083774956","https://openalex.org/W2158464203","https://openalex.org/W2078971842","https://openalex.org/W1656092346","https://openalex.org/W2348231333","https://openalex.org/W2474947407","https://openalex.org/W1577151476","https://openalex.org/W1531645310","https://openalex.org/W2079718016"],"abstract_inverted_index":{"Abstract":[0],"It":[1],"has":[2],"been":[3],"known":[4],"for":[5,25],"more":[6],"than":[7],"thirty":[8],"years":[9],"that":[10,41],"the":[11,26,39,42,53,68],"degree":[12,43,54],"of":[13,17,33,44,55,59],"a":[14,21,31,56,64],"non-standard":[15,57],"model":[16,58],"true":[18,60],"arithmetic":[19,27],"is":[20,36,48],"subuniform":[22],"upper":[23],"bound":[24],"sets":[28],"(suub).":[29],"Here":[30],"notion":[32],"generic":[34],"enumeration":[35,47],"presented":[37],"with":[38],"property":[40],"such":[45],"an":[46,49],"suub":[50],"but":[51],"not":[52],"arithmetic.":[61],"This":[62],"answers":[63],"question":[65],"posed":[66],"in":[67],"literature.":[69]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}