{"id":"https://openalex.org/W1992833344","doi":"https://doi.org/10.2307/2273867","title":"Remarks on weak notions of saturation in models of Peano arithmetic","display_name":"Remarks on weak notions of saturation in models of Peano arithmetic","publication_year":1987,"publication_date":"1987-03-01","ids":{"openalex":"https://openalex.org/W1992833344","doi":"https://doi.org/10.2307/2273867","mag":"1992833344"},"language":"en","primary_location":{"id":"doi:10.2307/2273867","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273867","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/A5004178046","display_name":"Matt Kaufmann","orcid":"https://orcid.org/0009-0004-5667-4888"},"institutions":[{"id":"https://openalex.org/I2800736688","display_name":"Burroughs Wellcome Fund","ror":"https://ror.org/01d35cw23","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I2800736688"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matt Kaufmann","raw_affiliation_strings":["Austin Research Center, Burroughs Corporation, Austin, Texas 78727"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Austin Research Center, Burroughs Corporation, Austin, Texas 78727","institution_ids":["https://openalex.org/I2800736688"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091663311","display_name":"James H. Schmerl","orcid":"https://orcid.org/0000-0003-0545-8339"},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James H. Schmerl","raw_affiliation_strings":["Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268","institution_ids":["https://openalex.org/I140172145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9282,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.73909324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"52","issue":"1","first_page":"129","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9911999702453613,"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":0.9907000064849854,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.9344374537467957},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6801780462265015},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6551485657691956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.601043701171875},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5310041904449463},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.5247802138328552},{"id":"https://openalex.org/keywords/terminology","display_name":"Terminology","score":0.4808848202228546},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4319693148136139},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4229061007499695},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41688334941864014},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3626244068145752},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2539585530757904},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.08967870473861694},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0779384970664978}],"concepts":[{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.9344374537467957},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6801780462265015},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6551485657691956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.601043701171875},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5310041904449463},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.5247802138328552},{"id":"https://openalex.org/C547195049","wikidata":"https://www.wikidata.org/wiki/Q1725664","display_name":"Terminology","level":2,"score":0.4808848202228546},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4319693148136139},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4229061007499695},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41688334941864014},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3626244068145752},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2539585530757904},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.08967870473861694},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0779384970664978},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273867","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273867","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/1183742315","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183742315","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":15,"referenced_works":["https://openalex.org/W98284338","https://openalex.org/W119327327","https://openalex.org/W143957234","https://openalex.org/W182686285","https://openalex.org/W1602067282","https://openalex.org/W2002502277","https://openalex.org/W2022298124","https://openalex.org/W2093435953","https://openalex.org/W2167687907","https://openalex.org/W2323760421","https://openalex.org/W2484395284","https://openalex.org/W2498473121","https://openalex.org/W2574346280","https://openalex.org/W2969873114","https://openalex.org/W3152223825"],"related_works":["https://openalex.org/W171744056","https://openalex.org/W1577881803","https://openalex.org/W2115117868","https://openalex.org/W3136886172","https://openalex.org/W4301007153","https://openalex.org/W4247822881","https://openalex.org/W4249882524","https://openalex.org/W3139378101","https://openalex.org/W1986326495","https://openalex.org/W2054510680"],"abstract_inverted_index":{"This":[0],"paper":[1,8],"is":[2,112,124,177,189,226,248],"a":[3,172,219],"sequel":[4],"to":[5,61,101,240],"our":[6],"earlier":[7],"[2]":[9,135,201],"entitled":[10],"Saturation":[11],"and":[12,85,115,158,233,243],"simple":[13,55,184,223],"extensions":[14],"of":[15,17,28,42,48,105,140,146,187,216,253,260],"models":[16,47,74,79,104,118,139,256,259],"Peano":[18,261],"arithmetic":[19],".":[20,94],"Among":[21],"other":[22,116],"things,":[23],"we":[24,38,66,97,130,196],"will":[25],"answer":[26,62,131,197],"some":[27,91],"the":[29,40,77,109,121,144,241],"questions":[30,133],"that":[31,70,72,204],"were":[32],"left":[33],"open":[34],"there.":[35],"In":[36,95,128],"\u00a71":[37,252],"consider":[39],"question":[41,199],"whether":[43],"there":[44],"are":[45,58,75,81,87,149,161,235,258],"lofty":[46,78],"PA":[49,106,141,217],"which":[50,80,86,108,120,160,176,188,225],"have":[51],"no":[52],"recursively":[53,83,113,126,167,179],"saturated,":[54],"extensions.":[56],"We":[57,169],"still":[59],"unable":[60],"this":[63,147],"question;":[64],"but":[65,153,165,181],"do":[67],"show":[68],"in":[69,107,119,143,194,251],"section":[71],"these":[73],"precisely":[76],"not":[82,125,154,166,178,227,244],"saturated":[84,180],"\u03ba":[88,93,207,213,220,228],"-like":[89],"for":[90,205],"regular":[92,206],"\u00a72":[96],"use":[98],"diagonal":[99],"methods":[100],"produce":[102],"minimal":[103,117],"standard":[110,122],"cut":[111,123],"definable,":[114],"definable.":[127],"\u00a73":[129],"two":[132],"from":[134,200],"by":[136,202],"exhibiting":[137],"countable":[138],"which,":[142],"terminology":[145,234],"paper,":[148],"uniformly":[150],"\u03c9":[151,156,163],"-lofty":[152,157,164],"continuously":[155,162],"others":[159],"saturated.":[168],"also":[170],"construct":[171],"model":[173,215],"(assuming":[174],"\u25c7)":[175],"every":[182,212],"proper,":[183,222],"cofinal":[185],"extension":[186,224],"\u2135":[190,209],"1":[191,210],"-saturated.":[192,230],"Finally,":[193],"\u00a74":[195],"another":[198],"proving":[203],"\u2265":[208],";":[211],"-saturated":[214,221],"has":[218],"+":[229],"Our":[231],"notation":[232],"quite":[236],"standard.":[237],"Anything":[238],"unfamiliar":[239],"reader":[242],"adequately":[245],"denned":[246],"here":[247],"probably":[249],"defined":[250],"[2].":[254],"All":[255],"considered":[257],"arithmetic.":[262]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}