{"id":"https://openalex.org/W2086001190","doi":"https://doi.org/10.2307/2275178","title":"Superstable differential fields","display_name":"Superstable differential fields","publication_year":1992,"publication_date":"1992-03-01","ids":{"openalex":"https://openalex.org/W2086001190","doi":"https://doi.org/10.2307/2275178","mag":"2086001190"},"language":"en","primary_location":{"id":"doi:10.2307/2275178","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275178","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/A5089545856","display_name":"Anthony L. Pillay","orcid":"https://orcid.org/0000-0001-8812-163X"},"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":"A. Pillay","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, E-mail:","Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, E-mail: pillay@irishmvs.bitnet"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, E-mail:","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, E-mail: pillay@irishmvs.bitnet","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038556250","display_name":"Zeljka Sokolovic","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":false,"raw_author_name":"\u017d. Sokolovi\u0107","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, E-mail:","Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, E-mail: zeljko@cartan.math.nd.edu"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, E-mail:","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, E-mail: zeljko@cartan.math.nd.edu","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089545856"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":null,"apc_paid":null,"fwci":0.6178,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.65935214,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"57","issue":"1","first_page":"97","last_page":"108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9965999722480774,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9965999722480774,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9918000102043152,"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/quantifier-elimination","display_name":"Quantifier elimination","score":0.8299225568771362},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7767938375473022},{"id":"https://openalex.org/keywords/differential-algebra","display_name":"Differential algebra","score":0.6473748683929443},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6266319155693054},{"id":"https://openalex.org/keywords/algebraically-closed-field","display_name":"Algebraically closed field","score":0.6216737031936646},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5965322852134705},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5893120169639587},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5863813161849976},{"id":"https://openalex.org/keywords/algebraic-differential-equation","display_name":"Algebraic differential equation","score":0.5168169736862183},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.509783923625946},{"id":"https://openalex.org/keywords/algebraic-closure","display_name":"Algebraic closure","score":0.5051537156105042},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4873214662075043},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4787951409816742},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4148009419441223},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38988494873046875},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21977055072784424},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.20790019631385803},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.18623536825180054},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.12359240651130676},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12039452791213989},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10837799310684204}],"concepts":[{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.8299225568771362},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7767938375473022},{"id":"https://openalex.org/C139080492","wikidata":"https://www.wikidata.org/wiki/Q7756337","display_name":"Differential algebra","level":2,"score":0.6473748683929443},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6266319155693054},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.6216737031936646},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5965322852134705},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5893120169639587},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5863813161849976},{"id":"https://openalex.org/C97145343","wikidata":"https://www.wikidata.org/wiki/Q4723995","display_name":"Algebraic differential equation","level":5,"score":0.5168169736862183},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.509783923625946},{"id":"https://openalex.org/C182327082","wikidata":"https://www.wikidata.org/wiki/Q428290","display_name":"Algebraic closure","level":5,"score":0.5051537156105042},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4873214662075043},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4787951409816742},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4148009419441223},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38988494873046875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21977055072784424},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.20790019631385803},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.18623536825180054},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.12359240651130676},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12039452791213989},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10837799310684204},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2275178","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275178","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/1183743893","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743893","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":9,"referenced_works":["https://openalex.org/W1554760224","https://openalex.org/W2014553533","https://openalex.org/W2037142577","https://openalex.org/W2081719649","https://openalex.org/W2314385873","https://openalex.org/W2316690454","https://openalex.org/W2319921428","https://openalex.org/W3198599232","https://openalex.org/W4213165369"],"related_works":["https://openalex.org/W1561989231","https://openalex.org/W2035153735","https://openalex.org/W97461773","https://openalex.org/W3030441133","https://openalex.org/W2782497445","https://openalex.org/W4287775153","https://openalex.org/W3156405290","https://openalex.org/W143396627","https://openalex.org/W4226470139","https://openalex.org/W2086001190"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,55,135],"study":[4],"differential":[5,25,49,76,100,128,170,201,208],"fields":[6,143],"of":[7,36,68,91,123,130,140,148,166,181,193],"characteristic":[8],"0":[9],"(with":[10],"perhaps":[11],"additional":[12],"structure)":[13],"whose":[14],"theory":[15,139,156],"is":[16,21,40,51,88,106,144,173,213,234],"superstable.":[17],"Our":[18,63,86],"main":[19,150],"result":[20,64,87,151],"that":[22,46,73,97,160,224],"such":[23],"a":[24,47,74,89,115,225,229],"field":[26,50,77,101,171,227],"has":[27,81,228],"no":[28,82],"proper":[29,83],"strongly":[30,162],"normal":[31,163],"extensions":[32],"in":[33,120],"the":[34,44,57,95,121,127,138,191,222],"sense":[35,122],"Kolchin":[37],"[K1].":[38],"This":[39],"an":[41,167,178],"approximation":[42],"to":[43,60,94,206],"conjecture":[45,59],"superstable":[48,226],"differentially":[52,141],"closed":[53,142,169],"(although":[54],"believe":[56],"full":[58],"be":[61],"false).":[62],"improves":[65],"earlier":[66],"work":[67],"Michaux":[69],"[Mi]":[70],"who":[71],"proved":[72],"(plain)":[75],"with":[78,103],"quantifier":[79,104,109],"elimination":[80,105],"Picard-Vessiot":[84],"extension.":[85],"generalisation":[90],"Michaux's,":[92],"due":[93],"fact":[96,223],"any":[98,161],"plain":[99],"K":[102,113,119,131,172,176,189,194,204,218],"\u03c9-stable.":[107],"(Any":[108],"free":[110],"type":[111,117,232],"over":[112,118,175,187,203,217],"defines":[114],"unique":[116,230],"dc(":[124],"k":[125],"),":[126,219],"closure":[129],",":[132,190,195],"and":[133,220],"as":[134],"mention":[136],"below":[137],"\u03c9-stable.)":[145],"The":[146],"proof":[147],"our":[149],"depends":[152],"on":[153,210],"(i)":[154],"Kolchin's":[155],"[K3]":[157],"which":[158,233],"states":[159],"extension":[164],"L":[165],"algebraically":[168],"generated":[174],"by":[177],"element":[179],"\u03b7":[180,197],"some":[182,199],"algebraic":[183],"group":[184],"G":[185,211,215],"defined":[186],"C":[188],"constants":[192],"where":[196],"satisfies":[198],"specific":[200],"equations":[202],"related":[205],"invariant":[207],"forms":[209],"(\u03b7":[212],"\u201c":[214],"-primitive\u201d":[216],"(ii)":[221],"generic":[231],"semiregular.":[235]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}