{"id":"https://openalex.org/W2118388414","doi":"https://doi.org/10.2178/jsl/1190150029","title":"Unique decomposition in classifiable theories","display_name":"Unique decomposition in classifiable theories","publication_year":2002,"publication_date":"2002-03-01","ids":{"openalex":"https://openalex.org/W2118388414","doi":"https://doi.org/10.2178/jsl/1190150029","mag":"2118388414"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1190150029","is_oa":true,"landing_page_url":"https://doi.org/10.2178/jsl/1190150029","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/0A6222C0A13C3E5B97D5CC2CA87D6CED/S0022481200009841a.pdf/div-class-title-unique-decomposition-in-classifiable-theories-div.pdf","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":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/0A6222C0A13C3E5B97D5CC2CA87D6CED/S0022481200009841a.pdf/div-class-title-unique-decomposition-in-classifiable-theories-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021510208","display_name":"Bradd Hart","orcid":null},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Bradd Hart","raw_affiliation_strings":["Department of Mathematics and Statistics, Mcmaster University, Hamilton, Ontario, Canada, L8S 4K1, E-mail:","McMaster university#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Mcmaster University, Hamilton, Ontario, Canada, L8S 4K1, E-mail:","institution_ids":["https://openalex.org/I98251732"]},{"raw_affiliation_string":"McMaster university#TAB#","institution_ids":["https://openalex.org/I98251732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053070582","display_name":"Ehud Hrushovski","orcid":"https://orcid.org/0000-0002-2761-6513"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ehud Hrushovski","raw_affiliation_strings":["Institute of Mathematics, The Hebrew University of Jerusalem, 91904, Israel, E-mail:","the Hebrew University of Jerusalem"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, The Hebrew University of Jerusalem, 91904, Israel, E-mail:","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"the Hebrew University of Jerusalem","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039592270","display_name":"M. Laskowski","orcid":"https://orcid.org/0000-0002-2516-6360"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael C. Laskowski","raw_affiliation_strings":["Mathematics Department, University of Maryland, College Park, MD 20742-4015, USA, E-mail:","University of Maryland"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of Maryland, College Park, MD 20742-4015, USA, E-mail:","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"University of Maryland","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021510208"],"corresponding_institution_ids":["https://openalex.org/I98251732"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.22087068,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"67","issue":"1","first_page":"61","last_page":"68"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.946399986743927,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.946399986743927,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9041000008583069,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.7186651229858398},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6862618327140808},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5870801210403442},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5359500050544739},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5150082111358643},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.45262855291366577},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.4451241195201874},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43406933546066284},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.42541196942329407},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3614206910133362},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3409659266471863},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3347814083099365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18650376796722412},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.13501060009002686}],"concepts":[{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.7186651229858398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6862618327140808},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5870801210403442},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5359500050544739},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5150082111358643},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.45262855291366577},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.4451241195201874},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43406933546066284},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.42541196942329407},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3614206910133362},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3409659266471863},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3347814083099365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18650376796722412},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.13501060009002686},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/jsl/1190150029","is_oa":true,"landing_page_url":"https://doi.org/10.2178/jsl/1190150029","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/0A6222C0A13C3E5B97D5CC2CA87D6CED/S0022481200009841a.pdf/div-class-title-unique-decomposition-in-classifiable-theories-div.pdf","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/1190150029","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1190150029","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:10.1.1.424.5881","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.424.5881","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www2.math.umd.edu/~laskow//Pubs/components.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.2178/jsl/1190150029","is_oa":true,"landing_page_url":"https://doi.org/10.2178/jsl/1190150029","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/0A6222C0A13C3E5B97D5CC2CA87D6CED/S0022481200009841a.pdf/div-class-title-unique-decomposition-in-classifiable-theories-div.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2118388414.pdf","grobid_xml":"https://content.openalex.org/works/W2118388414.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1991517235","https://openalex.org/W4239844957"],"related_works":["https://openalex.org/W4300828264","https://openalex.org/W3105928773","https://openalex.org/W2106480630","https://openalex.org/W177522066","https://openalex.org/W2962677089","https://openalex.org/W2101752691","https://openalex.org/W2402501407","https://openalex.org/W4236854827","https://openalex.org/W2067699663","https://openalex.org/W2167651941"],"abstract_inverted_index":{"By":[0],"a":[1,7,53,58],"classifiable":[2,60],"theory":[3,8,49,61],"we":[4,28,33,67,80,113,165],"shall":[5],"mean":[6,29],"which":[9,17,130],"is":[10,98,118,131,137,156],"superstable,":[11],"without":[12],"the":[13,35,44,106,172],"dimensional":[14],"order":[15,24],"property,":[16],"has":[18],"prime":[19,173],"models":[20,73,85,150],"over":[21,161,175],"pairs.":[22],"In":[23],"to":[25,120],"define":[26],"what":[27],"by":[30],"unique":[31],"decomposition,":[32],"remind":[34],"reader":[36],"of":[37,47,57,74,83,89,102,128,151],"several":[38],"definitions":[39],"and":[40,50,78,153],"results.":[41],"We":[42,123],"adopt":[43,125],"usual":[45],"conventions":[46],"stability":[48],"work":[51],"inside":[52],"large":[54],"saturated":[55,92],"model":[56,174],"fixed":[59,91],"T":[62,75,117,136,152],";":[63],"for":[64,72,144,171],"instance,":[65],"if":[66,135],"write":[68,166],"M":[69,77,97,139,142,154,159,162,167,169,176,179],"\u2286":[70,141],"N":[71,79,103],",":[76],"are":[81,149],"thinking":[82],"these":[84],"as":[86],"elementary":[87,100],"submodels":[88],"this":[90],"models;":[93],"so,":[94],"in":[95],"particular,":[96],"an":[99],"submodel":[101],".":[104,181],"Although":[105],"results":[107],"will":[108,114],"not":[109,132],"depend":[110],"on":[111],"it,":[112],"assume":[115],"that":[116],"countable":[119],"ease":[121],"notation.":[122],"do":[124],"one":[126],"piece":[127],"notation":[129],"completely":[133],"standard:":[134],"classifiable,":[138],"0":[140,163],"i":[143,145],"=":[146],"1,":[147],"2":[148,160,170,180],"1":[155,168,177],"independent":[157],"from":[158],"then":[164],"\u222a":[178]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
