{"id":"https://openalex.org/W2119801210","doi":"https://doi.org/10.2178/jsl/1294170992","title":"Iterative differential Galois theory in positive characteristic: A model theoretic approach","display_name":"Iterative differential Galois theory in positive characteristic: A model theoretic approach","publication_year":2011,"publication_date":"2011-01-04","ids":{"openalex":"https://openalex.org/W2119801210","doi":"https://doi.org/10.2178/jsl/1294170992","mag":"2119801210"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1294170992","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1294170992","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/A5053809006","display_name":"Javier A. Moreno","orcid":null},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Javier Moreno","raw_affiliation_strings":["Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon1, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France, E-mail:","Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France, E-mail: moreno@math.univ-lyonl.fr, URL: http/math.univ-lyonl.fr~moreno"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon1, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France, E-mail:","institution_ids":["https://openalex.org/I4210104796","https://openalex.org/I100532134"]},{"raw_affiliation_string":"Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France, E-mail: moreno@math.univ-lyonl.fr, URL: http/math.univ-lyonl.fr~moreno","institution_ids":["https://openalex.org/I4210104796","https://openalex.org/I100532134"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053809006"],"corresponding_institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210104796"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.16058154,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"76","issue":"1","first_page":"125","last_page":"142"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9986000061035156,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9986000061035156,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9976999759674072,"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/T11752","display_name":"Cancer Treatment and Pharmacology","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-galois-theory","display_name":"Differential Galois theory","score":0.8055380582809448},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7200736403465271},{"id":"https://openalex.org/keywords/galois-group","display_name":"Galois group","score":0.621590256690979},{"id":"https://openalex.org/keywords/galois-extension","display_name":"Galois extension","score":0.6106176376342773},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.5888558626174927},{"id":"https://openalex.org/keywords/differential-algebraic-geometry","display_name":"Differential algebraic geometry","score":0.5721898674964905},{"id":"https://openalex.org/keywords/normal-basis","display_name":"Normal basis","score":0.5380859375},{"id":"https://openalex.org/keywords/algebraic-differential-equation","display_name":"Algebraic differential equation","score":0.5366353988647461},{"id":"https://openalex.org/keywords/embedding-problem","display_name":"Embedding problem","score":0.5362808704376221},{"id":"https://openalex.org/keywords/fundamental-theorem-of-galois-theory","display_name":"Fundamental theorem of Galois theory","score":0.5184752345085144},{"id":"https://openalex.org/keywords/galois-module","display_name":"Galois module","score":0.46616774797439575},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4498264193534851},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.43652212619781494},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4233306646347046},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.42126837372779846},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4042423665523529},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4040926694869995},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3415181636810303},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.34013473987579346},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2667868733406067},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.1986408829689026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1933610439300537},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18781819939613342}],"concepts":[{"id":"https://openalex.org/C197968787","wikidata":"https://www.wikidata.org/wiki/Q2383624","display_name":"Differential Galois theory","level":4,"score":0.8055380582809448},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7200736403465271},{"id":"https://openalex.org/C67536143","wikidata":"https://www.wikidata.org/wiki/Q730384","display_name":"Galois group","level":2,"score":0.621590256690979},{"id":"https://openalex.org/C26204071","wikidata":"https://www.wikidata.org/wiki/Q2020004","display_name":"Galois extension","level":3,"score":0.6106176376342773},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.5888558626174927},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.5721898674964905},{"id":"https://openalex.org/C205567592","wikidata":"https://www.wikidata.org/wiki/Q3527199","display_name":"Normal basis","level":3,"score":0.5380859375},{"id":"https://openalex.org/C97145343","wikidata":"https://www.wikidata.org/wiki/Q4723995","display_name":"Algebraic differential equation","level":5,"score":0.5366353988647461},{"id":"https://openalex.org/C35435516","wikidata":"https://www.wikidata.org/wiki/Q5370016","display_name":"Embedding problem","level":3,"score":0.5362808704376221},{"id":"https://openalex.org/C78562435","wikidata":"https://www.wikidata.org/wiki/Q766522","display_name":"Fundamental theorem of Galois theory","level":4,"score":0.5184752345085144},{"id":"https://openalex.org/C145899342","wikidata":"https://www.wikidata.org/wiki/Q3427418","display_name":"Galois module","level":2,"score":0.46616774797439575},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4498264193534851},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.43652212619781494},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4233306646347046},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.42126837372779846},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4042423665523529},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4040926694869995},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3415181636810303},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.34013473987579346},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2667868733406067},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.1986408829689026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1933610439300537},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18781819939613342},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.2178/jsl/1294170992","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1294170992","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/1294170992","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1294170992","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:10.1.1.163.4109","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.163.4109","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.logique.jussieu.fr/modnet/Publications/Preprint%20server/papers/190/190.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.313.1581","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.313.1581","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0907.4559v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.591.8218","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.591.8218","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/40/75/62/PDF/IterativeDiffGaloisTheory.pdf","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":46,"referenced_works":["https://openalex.org/W2719155","https://openalex.org/W120723661","https://openalex.org/W139173061","https://openalex.org/W176367973","https://openalex.org/W234804402","https://openalex.org/W311000671","https://openalex.org/W355743254","https://openalex.org/W394295880","https://openalex.org/W1042189748","https://openalex.org/W1480542034","https://openalex.org/W1494321688","https://openalex.org/W1497483179","https://openalex.org/W1499179478","https://openalex.org/W1510765554","https://openalex.org/W1515420716","https://openalex.org/W1548944036","https://openalex.org/W1556189547","https://openalex.org/W1560726565","https://openalex.org/W1567200859","https://openalex.org/W1593582509","https://openalex.org/W1595305952","https://openalex.org/W1603468845","https://openalex.org/W1608732220","https://openalex.org/W1828839365","https://openalex.org/W1973360680","https://openalex.org/W1980662086","https://openalex.org/W1988342886","https://openalex.org/W2006192060","https://openalex.org/W2024549858","https://openalex.org/W2034949131","https://openalex.org/W2050466512","https://openalex.org/W2051077260","https://openalex.org/W2053706408","https://openalex.org/W2079302432","https://openalex.org/W2086001190","https://openalex.org/W2093279438","https://openalex.org/W2142614880","https://openalex.org/W2171605982","https://openalex.org/W2243983621","https://openalex.org/W2409501111","https://openalex.org/W3037314659","https://openalex.org/W4248119737","https://openalex.org/W4285719527","https://openalex.org/W6636294907","https://openalex.org/W6663881468","https://openalex.org/W6714412730"],"related_works":["https://openalex.org/W2730690530","https://openalex.org/W4380323552","https://openalex.org/W2189024741","https://openalex.org/W959740625","https://openalex.org/W4206315376","https://openalex.org/W2098184515","https://openalex.org/W1999806526","https://openalex.org/W3098615792","https://openalex.org/W2950187810","https://openalex.org/W1592091505"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"introduces":[3],"a":[4,52,74],"natural":[5],"extension":[6,57],"of":[7,46,54,58,84,88,91],"Kolchin's":[8],"differential":[9,16,48,60],"Galois":[10,70,107],"theory":[11,26,45,71,87],"to":[12,19],"positive":[13],"characteristic":[14],"iterative":[15,24,47,59,96],"fields,":[17,61],"generalizing":[18],"the":[20,23,37,43,85],"non-linear":[21],"case":[22],"Picard\u2013Vessiot":[25],"recently":[27],"developed":[28],"by":[29,42],"Matzat":[30],"and":[31,39,62,72],"van":[32],"der":[33],"Put.":[34],"We":[35,50],"use":[36,83],"methods":[38],"framework":[40],"provided":[41],"model":[44],"fields.":[49],"offer":[51],"definition":[53],"strongly":[55,103],"normal":[56,104],"then":[63],"prove":[64],"that":[65,73,101],"these":[66,110],"extensions":[67,105,108],"have":[68],"good":[69],"G":[75],"-primitive":[76],"element":[77],"theorem":[78],"holds.":[79],"In":[80],"addition,":[81],"making":[82],"basic":[86],"arc":[89],"spaces":[90],"algebraic":[92],"groups,":[93],"we":[94],"define":[95],"logarithmic":[97],"equations,":[98],"finally":[99],"proving":[100],"our":[102],"are":[106],"for":[109],"equations.":[111]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}