{"id":"https://openalex.org/W3083807189","doi":"https://doi.org/10.1215/00294527-2020-0013","title":"Definable Functions and Stratifications in Power-Bounded T -Convex Fields","display_name":"Definable Functions and Stratifications in Power-Bounded T -Convex Fields","publication_year":2020,"publication_date":"2020-09-01","ids":{"openalex":"https://openalex.org/W3083807189","doi":"https://doi.org/10.1215/00294527-2020-0013","mag":"3083807189"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-2020-0013","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00294527-2020-0013","pdf_url":null,"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":["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/A5018949573","display_name":"Erick Garc\u00eda Ram\u00edrez","orcid":"https://orcid.org/0000-0001-9030-5032"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Erick Garc\u00eda Ram\u00edrez","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018949573"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3852,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58967001,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"61","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9995999932289124,"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":0.9995999932289124,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9943000078201294,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9907000064849854,"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/bounded-function","display_name":"Bounded function","score":0.799873948097229},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7372919321060181},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6637104749679565},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6269087791442871},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49253949522972107},{"id":"https://openalex.org/keywords/convex-geometry","display_name":"Convex geometry","score":0.431325227022171},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.42642468214035034},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3803774416446686},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.366172194480896},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2881540060043335},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28658807277679443},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.27126544713974},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.12813043594360352},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.08505094051361084}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.799873948097229},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7372919321060181},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6637104749679565},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6269087791442871},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49253949522972107},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.431325227022171},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.42642468214035034},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3803774416446686},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.366172194480896},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2881540060043335},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28658807277679443},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.27126544713974},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.12813043594360352},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.08505094051361084},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1215/00294527-2020-0013","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00294527-2020-0013","pdf_url":null,"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:CULeuclid:euclid.ndjfl/1599638409","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1599638409","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":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1561989231","https://openalex.org/W1602070847","https://openalex.org/W1822440022","https://openalex.org/W1871045369","https://openalex.org/W2010757891","https://openalex.org/W2042400181","https://openalex.org/W2053215128","https://openalex.org/W2150394096","https://openalex.org/W2162052349","https://openalex.org/W2476658189","https://openalex.org/W2765895272","https://openalex.org/W2963042562","https://openalex.org/W2963462782","https://openalex.org/W3037994112","https://openalex.org/W3104521991","https://openalex.org/W4237551483","https://openalex.org/W4255831104","https://openalex.org/W4299599836","https://openalex.org/W4388397256"],"related_works":["https://openalex.org/W1793337513","https://openalex.org/W2296389180","https://openalex.org/W2280528715","https://openalex.org/W36492929","https://openalex.org/W4318719150","https://openalex.org/W2016297007","https://openalex.org/W2978694018","https://openalex.org/W1967098823","https://openalex.org/W4287548684","https://openalex.org/W3123643346"],"abstract_inverted_index":{"We":[0,59],"study":[1],"properties":[2],"of":[3,26,40,49,64,66],"definable":[4,54],"sets":[5],"and":[6,22,38],"functions":[7],"in":[8,56],"power-bounded":[9],"T":[10,27],"-convex":[11,28],"fields,":[12],"proving":[13],"that":[14,23,45],"the":[15,18,24],"latter":[16],"have":[17],"multidimensional":[19],"Jacobian":[20],"property":[21],"theory":[25],"fields":[29],"is":[30],"b":[31],"-minimal":[32],"with":[33],"centers.":[34],"Through":[35],"these":[36],"results":[37],"work":[39],"I.":[41],"Halupczok":[42],"we":[43],"ensure":[44],"a":[46,62],"certain":[47],"kind":[48],"geometrical":[50],"stratifications":[51],"exist":[52],"for":[53],"objects":[55],"said":[57],"fields.":[58],"then":[60],"discuss":[61],"number":[63],"applications":[65,70],"those":[67],"stratifications,":[68],"including":[69],"to":[71],"Archimedean":[72],"o-minimal":[73],"geometry.":[74]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2020-09-14T00:00:00"}