{"id":"https://openalex.org/W1963722974","doi":"https://doi.org/10.2178/jsl.7704010","title":"On algebraic closure in pseudofinite fields","display_name":"On algebraic closure in pseudofinite fields","publication_year":2012,"publication_date":"2012-11-02","ids":{"openalex":"https://openalex.org/W1963722974","doi":"https://doi.org/10.2178/jsl.7704010","mag":"1963722974"},"language":"en","primary_location":{"id":"doi:10.2178/jsl.7704010","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl.7704010","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0909.2189","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052863388","display_name":"\u00d6zlem Beyarslan","orcid":null},"institutions":[{"id":"https://openalex.org/I4405392","display_name":"Bo\u011fazi\u00e7i University","ror":"https://ror.org/03z9tma90","country_code":"TR","type":"education","lineage":["https://openalex.org/I4405392"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"\u00d6zlem Beyarslan","raw_affiliation_strings":["Department of Mathematics, Bo\u01e7azi\u00e7i University, 34342 Bebek, \u00cdstanbul, Turkey, E-mail:","Department of Mathematics, Bo\u01e7azi\u00e7i University, 34342 Bebek, \u00cdstanbul, Turkey, E-mail: ozlem.beyarslan@boun.edu.tr"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bo\u01e7azi\u00e7i University, 34342 Bebek, \u00cdstanbul, Turkey, E-mail:","institution_ids":["https://openalex.org/I4405392"]},{"raw_affiliation_string":"Department of Mathematics, Bo\u01e7azi\u00e7i University, 34342 Bebek, \u00cdstanbul, Turkey, E-mail: ozlem.beyarslan@boun.edu.tr","institution_ids":["https://openalex.org/I4405392"]}]},{"author_position":"last","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":["Department of Mathematics, Hebrew University at Jerusalem, 91904 Jerusalem, Israel, E-mail:","Department of Mathematics, Hebrew University at Jerusalem, 91904 Jerusalem, Israel, E-mail: ehud@math.huji.ac.il"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hebrew University at Jerusalem, 91904 Jerusalem, Israel, E-mail:","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"Department of Mathematics, Hebrew University at Jerusalem, 91904 Jerusalem, Israel, E-mail: ehud@math.huji.ac.il","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4193,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5810367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"77","issue":"4","first_page":"1057","last_page":"1066"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9937000274658203,"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":0.9937000274658203,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9912999868392944,"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":0.9715999960899353,"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/algebraic-closure","display_name":"Algebraic closure","score":0.9051169753074646},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.8800396919250488},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7551132440567017},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5932733416557312},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.5776987075805664},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5729731321334839},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.49878358840942383},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.48552632331848145},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.46191051602363586},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.44102826714515686},{"id":"https://openalex.org/keywords/substructure","display_name":"Substructure","score":0.4130634665489197},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31534484028816223},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2607347369194031},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1024063229560852},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.04647865891456604}],"concepts":[{"id":"https://openalex.org/C182327082","wikidata":"https://www.wikidata.org/wiki/Q428290","display_name":"Algebraic closure","level":5,"score":0.9051169753074646},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.8800396919250488},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7551132440567017},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5932733416557312},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.5776987075805664},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5729731321334839},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.49878358840942383},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48552632331848145},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.46191051602363586},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.44102826714515686},{"id":"https://openalex.org/C99679407","wikidata":"https://www.wikidata.org/wiki/Q56761637","display_name":"Substructure","level":2,"score":0.4130634665489197},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31534484028816223},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2607347369194031},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1024063229560852},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.04647865891456604},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.2178/jsl.7704010","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl.7704010","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:arXiv.org:0909.2189","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0909.2189","pdf_url":"https://arxiv.org/pdf/0909.2189","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"mag:1963722974","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/0909.2189.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CULeuclid:euclid.jsl/1350315576","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1350315576","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:10.1.1.245.7876","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.245.7876","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/0909.2189v1.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.0909.2189","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0909.2189","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0909.2189","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0909.2189","pdf_url":"https://arxiv.org/pdf/0909.2189","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1870712983","https://openalex.org/W1895185699","https://openalex.org/W2092230546","https://openalex.org/W2274120872","https://openalex.org/W4233055929","https://openalex.org/W4247556508"],"related_works":["https://openalex.org/W3167634872","https://openalex.org/W2058111974","https://openalex.org/W2124864827","https://openalex.org/W2949503432","https://openalex.org/W2077223329","https://openalex.org/W2138269517","https://openalex.org/W1993317508","https://openalex.org/W2078437137","https://openalex.org/W1558286746","https://openalex.org/W2098656864","https://openalex.org/W2236401661","https://openalex.org/W3014369595","https://openalex.org/W3105819957","https://openalex.org/W2950041517","https://openalex.org/W2952254384","https://openalex.org/W1574167599","https://openalex.org/W2963896245","https://openalex.org/W99701452","https://openalex.org/W1994176685"],"abstract_inverted_index":{"Abstract":[0],"We":[1,20],"study":[2],"the":[3,7,23,36,48,70,75],"automorphism":[4],"group":[5],"of":[6,10,14,25,38,47,50,74],"algebraic":[8,59,72],"closure":[9,60,73],"a":[11,15],"substructure":[12],"A":[13,30,57,68],"pseudo-finite":[16],"field":[17],"F":[18,41],".":[19,42],"show":[21,54],"that":[22,55],"behavior":[24],"this":[26],"group,":[27],"even":[28],"when":[29],"is":[31],"large,":[32],"depends":[33],"essentially":[34],"on":[35],"roots":[37],"unity":[39],"in":[40],"For":[43],"almost":[44],"all":[45],"completions":[46],"theory":[49],"pseudofinite":[51],"fields,":[52],"we":[53],"over":[56],",":[58],"agrees":[61],"with":[62],"definable":[63],"closure,":[64],"as":[65,67],"soon":[66],"contains":[69],"relative":[71],"prime":[76],"field.":[77]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
