{"id":"https://openalex.org/W2170859610","doi":"https://doi.org/10.1215/00294527-2143898","title":"Toward a Model Theory for Transseries","display_name":"Toward a Model Theory for Transseries","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2170859610","doi":"https://doi.org/10.1215/00294527-2143898","mag":"2170859610"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-2143898","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2143898","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-54/issue-3-4/Toward-a-Model-Theory-for-Transseries/10.1215/00294527-2143898.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-54/issue-3-4/Toward-a-Model-Theory-for-Transseries/10.1215/00294527-2143898.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Matthias Aschenbrenner","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthias Aschenbrenner","raw_affiliation_strings":["Aschenbrenner University of California, Los Angeles Los Angeles, California 90955 USA"],"affiliations":[{"raw_affiliation_string":"Aschenbrenner University of California, Los Angeles Los Angeles, California 90955 USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Lou van den Dries","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lou van den Dries","raw_affiliation_strings":["Aschenbrenner University of California, Los Angeles Los Angeles, California 90955 USA"],"affiliations":[{"raw_affiliation_string":"Aschenbrenner University of California, Los Angeles Los Angeles, California 90955 USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":null,"display_name":"Joris van der Hoeven","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joris van der Hoeven","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":1.791,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.85028743,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"54","issue":"3-4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.8180000185966492,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.8180000185966492,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.03180000185966492,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.030400000512599945,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/laurent-series","display_name":"Laurent series","score":0.8004999756813049},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.6840000152587891},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.6306999921798706},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5514000058174133},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5436000227928162},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.47269999980926514},{"id":"https://openalex.org/keywords/differential-algebra","display_name":"Differential algebra","score":0.4357999861240387},{"id":"https://openalex.org/keywords/field-theory","display_name":"Field theory (psychology)","score":0.39750000834465027}],"concepts":[{"id":"https://openalex.org/C184311908","wikidata":"https://www.wikidata.org/wiki/Q425432","display_name":"Laurent series","level":2,"score":0.8004999756813049},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.6840000152587891},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.6306999921798706},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5514000058174133},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5436000227928162},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49129998683929443},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.47269999980926514},{"id":"https://openalex.org/C139080492","wikidata":"https://www.wikidata.org/wiki/Q7756337","display_name":"Differential algebra","level":2,"score":0.4357999861240387},{"id":"https://openalex.org/C187268509","wikidata":"https://www.wikidata.org/wiki/Q1402884","display_name":"Field theory (psychology)","level":2,"score":0.39750000834465027},{"id":"https://openalex.org/C2779851814","wikidata":"https://www.wikidata.org/wiki/Q5358916","display_name":"Elementary theory","level":2,"score":0.3788999915122986},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.376800000667572},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.3743000030517578},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35760000348091125},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.349700003862381},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.29159998893737793},{"id":"https://openalex.org/C2779782106","wikidata":"https://www.wikidata.org/wiki/Q4724020","display_name":"Algebraic theory","level":3,"score":0.28220000863075256},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2754000127315521},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.263700008392334},{"id":"https://openalex.org/C97145343","wikidata":"https://www.wikidata.org/wiki/Q4723995","display_name":"Algebraic differential equation","level":5,"score":0.2597000002861023},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2572999894618988},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.25130000710487366},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.2500999867916107}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1215/00294527-2143898","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2143898","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-54/issue-3-4/Toward-a-Model-Theory-for-Transseries/10.1215/00294527-2143898.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1112.5237","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1112.5237","pdf_url":"https://arxiv.org/pdf/1112.5237","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":null,"raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1376053768","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1376053768","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:HAL:hal-02350418v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02350418","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Notre Dame Journal of Formal Logic, 2013, 54 (3-4), pp.279-310. &#x27E8;10.1215/00294527-2143898&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1215/00294527-2143898","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2143898","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-54/issue-3-4/Toward-a-Model-Theory-for-Transseries/10.1215/00294527-2143898.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4118784115","display_name":"Math\u00e9matiques, Analyse, G\u00e9om\u00e9trie, Interfaces, eXactes","funder_award_id":"ANR-09-JCJC-0098","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7174746683","display_name":null,"funder_award_id":"0556197","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7455992287","display_name":"MODEL THEORY AND ALGEBRA","funder_award_id":"0969642","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2170859610.pdf","grobid_xml":"https://content.openalex.org/works/W2170859610.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W943250386","https://openalex.org/W999861136","https://openalex.org/W1568625975","https://openalex.org/W1822440022","https://openalex.org/W1973290863","https://openalex.org/W1996490280","https://openalex.org/W2006875261","https://openalex.org/W2007519455","https://openalex.org/W2017769265","https://openalex.org/W2041531262","https://openalex.org/W2042400181","https://openalex.org/W2068293635","https://openalex.org/W2074771628","https://openalex.org/W2084375669","https://openalex.org/W2090497251","https://openalex.org/W2091741226","https://openalex.org/W2092147450","https://openalex.org/W2129688799","https://openalex.org/W2138250274","https://openalex.org/W2143993716","https://openalex.org/W2168485982","https://openalex.org/W2319305328","https://openalex.org/W2333144356","https://openalex.org/W2334045162","https://openalex.org/W2480175691","https://openalex.org/W2963808377","https://openalex.org/W2979335218","https://openalex.org/W3162566251","https://openalex.org/W4237811246","https://openalex.org/W4252958890"],"related_works":[],"abstract_inverted_index":{"The":[0],"differential":[1,41],"field":[2,7,42],"of":[3,8,33,39],"transseries":[4],"extends":[5],"the":[6,34],"real":[9],"Laurent":[10],"series":[11],"and":[12,22,36,43],"occurs":[13],"in":[14],"various":[15],"contexts:":[16],"asymptotic":[17],"expansions,":[18],"analytic":[19],"vector":[20],"fields,":[21],"o-minimal":[23],"structures,":[24],"to":[25,48],"name":[26],"a":[27],"few.":[28],"We":[29],"give":[30],"an":[31],"overview":[32],"algebraic":[35],"model-theoretic":[37],"aspects":[38],"this":[40],"report":[44],"on":[45],"our":[46],"efforts":[47],"understand":[49],"its":[50],"elementary":[51],"theory.":[52]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2016-06-24T00:00:00"}
