{"id":"https://openalex.org/W1982022674","doi":"https://doi.org/10.2178/jsl/1080938838","title":"Forking and independence in o-minimal theories","display_name":"Forking and independence in o-minimal theories","publication_year":2004,"publication_date":"2004-03-01","ids":{"openalex":"https://openalex.org/W1982022674","doi":"https://doi.org/10.2178/jsl/1080938838","mag":"1982022674"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1080938838","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1080938838","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/A5077529007","display_name":"Alfred Dolich","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alfred Dolich","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706, USA, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706, USA, E-mail:","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5077529007"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":2.0518,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.85893228,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"69","issue":"1","first_page":"215","last_page":"240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9955999851226807,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9955999851226807,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9941999912261963,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9854999780654907,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.8186173439025879},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7364052534103394},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.683411180973053},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6759377717971802},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6708378195762634},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.6630828380584717},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4590607285499573},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.429095983505249},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4103223979473114},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4103134274482727},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4022795557975769},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3439478874206543},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.26748719811439514},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18675026297569275},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09387743473052979}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.8186173439025879},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7364052534103394},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.683411180973053},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6759377717971802},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6708378195762634},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.6630828380584717},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4590607285499573},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.429095983505249},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4103223979473114},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4103134274482727},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4022795557975769},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3439478874206543},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.26748719811439514},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18675026297569275},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09387743473052979},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1080938838","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1080938838","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/1080938838","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1080938838","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":6,"referenced_works":["https://openalex.org/W1988668887","https://openalex.org/W2010757891","https://openalex.org/W2021341336","https://openalex.org/W2077363173","https://openalex.org/W2162052349","https://openalex.org/W4212846603"],"related_works":["https://openalex.org/W2366107444","https://openalex.org/W4388145910","https://openalex.org/W2381570729","https://openalex.org/W1976205134","https://openalex.org/W4248336175","https://openalex.org/W3009369890","https://openalex.org/W2031260042","https://openalex.org/W2391445434","https://openalex.org/W4312490297","https://openalex.org/W2062212388"],"abstract_inverted_index":{"In":[0,56,292],"the":[1,46,63,92,114,121,149,168,176,212,218,231,245,296,324,370,388,397],"following":[2],"we":[3,90,105,318,328],"try":[4],"to":[5,87,95,227,243,277,344,385],"answer":[6],"a":[7,76,132,141,145,158,250,266,283,309],"simple":[8,49,54,66,117,179,325],"question,":[9],"\u201cwhat":[10,22],"does":[11],"forking":[12,307,333,373],"look":[13,273,345],"like":[14],"in":[15,35,125,256,275,312,376],"an":[16,36],"o-minimal":[17,37,201,398],"theory\u201d,":[18],"or":[19],"more":[20],"generally,":[21],"kinds":[23,30],"of":[24,26,31,41,48,53,65,78,102,109,116,123,138,140,165,167,178,247,262,268,285,295,314,339,348,351,362,372,387,393],"notions":[25,361],"independence":[27,79,248,269,286,363],"with":[28,45,211,323],"what":[29,100,229,263],"properties":[32],"are":[33,230,319,334],"admissible":[34],"theory?\u201d":[38],"The":[39],"motivation":[40],"these":[42,207,340,377],"question":[43],"begin":[44],"study":[47,115,244],"theories":[50,67,74,103,180,202,233,280,350],"and":[51,59,127,237,306,332,364,374],"generalizations":[52],"theories.":[55,399],"[3]":[57],"Kim":[58],"Pillay":[60],"prove":[61],"that":[62,144,175,187,200,279,304,330],"class":[64,137,177],"may":[68],"be":[69,197,205,288],"described":[70],"exactly":[71],"as":[72,94,192],"those":[73],"bearing":[75,281],"notion":[77,267,284],"satisfying":[80,162],"various":[81,163],"axioms.":[82],"Thus":[83,223],"it":[84,195,300],"is":[85,225,239,354,382],"natural":[86],"ask,":[88,228],"if":[89,154],"weaken":[91],"assumptions":[93],"which":[96,352],"axioms":[97,264],"must":[98],"hold,":[99],"kind":[101],"do":[104,191],"get?":[106],"Another":[107],"source":[108],"motivation,":[110],"also":[111,186,366],"stemming":[112],"from":[113,120],"theories,":[118,395],"comes":[119],"work":[122],"Shelah":[124,130,173,255],"[8]":[126],"[7].":[128],"Here":[129],"addresses":[131],"\u201cclassification\u201d":[133],"type":[134,152],"problem":[135],"for":[136,265,274,346],"models":[139,166],"theory,":[142],"showing":[143],"theory":[146,210,251],"will":[147,216],"have":[148,217],"appropriate":[150],"\u201cstructure\u201d":[151,183],"property":[153,215,221],"one":[155,224,238,270,343,357,381,386],"can":[156,203,358],"construct":[157,359],"partially":[159],"ordered":[160],"set,":[161],"properties,":[164],"theory.":[169],"Using":[170],"this":[171,182,235,380],"criterion":[172],"shows":[174],"has":[181],"property,":[184],"yet":[185],"several":[188],"non-simple":[189,232,349,394],"examples":[190],"well":[193,336,390],"(though":[194],"should":[196,271,287],"pointed":[198],"out":[199],"not":[204],"among":[206],"since":[208],"any":[209],"strict":[213],"order":[214,276],"corresponding":[219],"\u201cnon-structure\u201d":[220],"[8]).":[222],"lead":[226,342,384],"meeting":[234],"criterion,":[236],"once":[240],"again":[241],"led":[242],"types":[246],"relation":[249],"might":[252],"bear.":[253],"Finally,":[254],"[6]":[257],"provides":[258],"some":[259],"possible":[260],"definitions":[261],"possibly":[272],"hope":[278],"such":[282],"amenable":[289],"closer":[290],"analysis.":[291],"studying":[293],"all":[294,313],"above":[297],"mentioned":[298],"situations":[299],"readily":[301],"becomes":[302],"clear":[303],"dividing":[305,331,375],"play":[308],"central":[310],"role":[311],"them,":[315],"even":[316],"though":[317],"no":[320],"longer":[321],"dealing":[322],"case":[326],"where":[327,356],"know":[329],"very":[335],"behaved.":[337],"All":[338],"considerations":[341],"classes":[347,392],"something":[353,368],"known":[355],"interesting":[360],"consequently":[365],"say":[367],"about":[369],"nature":[371],"contexts.":[378],"Given":[379],"naturally":[383],"most":[389],"behaved":[391],"namely":[396]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2026-07-14T08:27:34.040176","created_date":"2025-10-10T00:00:00"}
