{"id":"https://openalex.org/W2028895622","doi":"https://doi.org/10.2307/2274950","title":"On models of the elementary theory of (Z, +, 1)","display_name":"On models of the elementary theory of (Z, +, 1)","publication_year":1990,"publication_date":"1990-03-01","ids":{"openalex":"https://openalex.org/W2028895622","doi":"https://doi.org/10.2307/2274950","mag":"2028895622"},"language":"en","primary_location":{"id":"doi:10.2307/2274950","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274950","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/A5074274651","display_name":"Mark Nadel","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mark Nadel","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556","Department of Mathematics University of Notre Dame Notre Dame Indiana 46556"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Department of Mathematics University of Notre Dame Notre Dame Indiana 46556","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019899729","display_name":"Jonathan Stavi","orcid":null},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Jonathan Stavi","raw_affiliation_strings":["Department of Mathematics, Bar Ilan University, Ramat Gan, Israel","Department\u00a0of Mathematics, Bar-Ilan University, Ramat Gan, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bar Ilan University, Ramat Gan, Israel","institution_ids":["https://openalex.org/I13955877"]},{"raw_affiliation_string":"Department\u00a0of Mathematics, Bar-Ilan University, Ramat Gan, Israel","institution_ids":["https://openalex.org/I13955877"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074274651"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":null,"apc_paid":null,"fwci":0.3764,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.60827193,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"55","issue":"1","first_page":"1","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9969000220298767,"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":0.9969000220298767,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9739000201225281,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9689000248908997,"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/mathematics","display_name":"Mathematics","score":0.7939309477806091},{"id":"https://openalex.org/keywords/homogeneity","display_name":"Homogeneity (statistics)","score":0.7379622459411621},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7034975290298462},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.634363055229187},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.5331026315689087},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.5327126383781433},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5172446370124817},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4653886556625366},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4285472631454468},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42547303438186646},{"id":"https://openalex.org/keywords/continuum-hypothesis","display_name":"Continuum hypothesis","score":0.41337817907333374},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4122988283634186},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17291924357414246},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11467298865318298}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7939309477806091},{"id":"https://openalex.org/C142259097","wikidata":"https://www.wikidata.org/wiki/Q5891314","display_name":"Homogeneity (statistics)","level":2,"score":0.7379622459411621},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7034975290298462},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.634363055229187},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.5331026315689087},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.5327126383781433},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5172446370124817},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4653886556625366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4285472631454468},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42547303438186646},{"id":"https://openalex.org/C96488702","wikidata":"https://www.wikidata.org/wiki/Q208416","display_name":"Continuum hypothesis","level":2,"score":0.41337817907333374},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4122988283634186},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17291924357414246},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11467298865318298},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274950","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274950","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/1183743181","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743181","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W40029885","https://openalex.org/W591591544","https://openalex.org/W1511526676","https://openalex.org/W1978423759","https://openalex.org/W2003868429","https://openalex.org/W2006904309","https://openalex.org/W2092937228","https://openalex.org/W2105505307","https://openalex.org/W2152863911","https://openalex.org/W2163888089","https://openalex.org/W2799061192","https://openalex.org/W4256112807","https://openalex.org/W4293117209"],"related_works":["https://openalex.org/W1985493589","https://openalex.org/W1877127512","https://openalex.org/W2016460164","https://openalex.org/W2279499033","https://openalex.org/W2024769114","https://openalex.org/W2131337804","https://openalex.org/W2113840635","https://openalex.org/W2034208453","https://openalex.org/W626248467","https://openalex.org/W2921213219"],"abstract_inverted_index":{"Let":[0],"T":[1,22,37,104,140,180,233],"1":[2,16,23,38,105,141,196,234],"be":[3,68],"the":[4,9,13,78,97,120,131,138,145,190,193,200,219,254],"complete":[5],"first-order":[6],"theory":[7,85,139,165],"of":[8,12,36,48,74,80,82,89,100,103,119,130,148,156,168,179,192,202,208,221,236],"additive":[10],"group":[11],"integers":[14],"with":[15],"as":[17,69,71,150],"distinguished":[18],"element":[19],"(in":[20],"symbols,":[21],"=":[24,181],"Th(Z,":[25,182],"+,":[26],"1)).":[27],"In":[28,123,170],"this":[29,127,209],"paper":[30,210],"we":[31,224,252],"prove":[32],"that":[33,65,95,158,175,189,232],"all":[34,101,177],"models":[35,102,178],"are":[39,106,184],"\u2135":[40,110,185],"0":[41,111,186],"-homogeneous":[42],"(\u00a72),":[43],"classify":[44],"them":[45],"(and":[46],"lists":[47],"elements":[49],"in":[50,163,218],"them)":[51],"up":[52,247],"to":[53,125,245],"isomorphism":[54],"or":[55],"L":[56],"\u221e":[57],"\u03ba":[58],"-equivalence":[59],"(\u00a7\u00a73":[60],"and":[61,63,91,136,212,229,242,256],"4)":[62],"show":[64,94],"they":[66],"may":[67],"complex":[70],"arbitrary":[72],"sets":[73],"real":[75],"numbers":[76],"from":[77,226],"point":[79],"view":[81],"admissible":[83],"set":[84],"(\u00a75).":[86],"The":[87,204],"results":[88,147,207],"\u00a7\u00a72":[90],"5":[92],"together":[93],"while":[96],"Scott":[98,134],"heights":[99,135],"\u2264":[107],"\u03c9":[108],"(by":[109],"-homogeneity)":[112],"their":[113],"HYP-heights":[114],"form":[115],"an":[116,151],"unbounded":[117],"subset":[118],"cardinal":[121],".":[122],"addition":[124],"providing":[126],"unusual":[128],"example":[129,152],"relation":[132],"between":[133],"HYP-heights,":[137],"has":[142],"served":[143],"(using":[144],"homogeneity":[146],"\u00a72)":[149],"for":[153,162,195,199,239],"certain":[154],"combinations":[155],"properties":[157],"people":[159],"had":[160],"looked":[161],"stability":[164,240],"(see":[166],"end":[167],"\u00a74).":[169],"\u00a76":[171],"it":[172],"is":[173,197,235],"shown":[174],"not":[176],"+)":[183],"-homogeneous,":[187],"so":[188],"availability":[191],"constant":[194],"essential":[198],"result":[201],"\u00a72.":[203],"two":[205],"main":[206],"(2.2":[211],"essentially":[213],"Theorem":[214],"5.3)":[215],"were":[216,243],"obtained":[217],"summer":[220],"1979.":[222],"Later":[223],"learnt":[225],"Victor":[227],"Harnik":[228],"Julia":[230],"Knight":[231],"some":[237,258],"interest":[238],"theory,":[241],"encouraged":[244],"write":[246],"our":[248],"proofs.":[249],"During":[250],"1982/3":[251],"improved":[253],"proofs":[255],"added":[257],"results.":[259]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}