{"id":"https://openalex.org/W2059214986","doi":"https://doi.org/10.1215/00294527-1626527","title":"On the Elementary Theory of Restricted Real and Imaginary Parts of Holomorphic Functions","display_name":"On the Elementary Theory of Restricted Real and Imaginary Parts of Holomorphic Functions","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2059214986","doi":"https://doi.org/10.1215/00294527-1626527","mag":"2059214986"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1626527","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/P4310315572","https://openalex.org/P4310315698"],"host_organization_lineage_names":["Duke University","Duke University Press"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1215/00294527-1626527","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030771991","display_name":"Hassan Sfouli","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hassan Sfouli","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5030771991"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":4,"citation_normalized_percentile":{"value":0.57667,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":78,"max":80},"biblio":{"volume":"53","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9997,"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":0.9997,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.998,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9969,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/real-number","display_name":"Real number","score":0.4857512}],"concepts":[{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.9004259},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6850232},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.51019144},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.50756824},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.4857512},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4025107},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38342327},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3452536},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1626527","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/P4310315572","https://openalex.org/P4310315698"],"host_organization_lineage_names":["Duke University","Duke University Press"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1336586238","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-1/On-the-Elementary-Theory-of-Restricted-Real-and-Imaginary-Parts/10.1215/00294527-1626527.pdf","source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (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":["Cornell University"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1626527","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/P4310315572","https://openalex.org/P4310315698"],"host_organization_lineage_names":["Duke University","Duke University Press"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":7,"referenced_works":["https://openalex.org/W1530671557","https://openalex.org/W1553142094","https://openalex.org/W1586233811","https://openalex.org/W1997612982","https://openalex.org/W2144033225","https://openalex.org/W2314912482","https://openalex.org/W4298290503"],"related_works":["https://openalex.org/W4248353673","https://openalex.org/W4237698157","https://openalex.org/W4226018956","https://openalex.org/W3094515845","https://openalex.org/W2982338311","https://openalex.org/W2952868792","https://openalex.org/W2295512640","https://openalex.org/W2211201902","https://openalex.org/W2089223129","https://openalex.org/W2036109498"],"abstract_inverted_index":{"We":[0],"show":[1,67],"that":[2,68],"the":[3,25,36,41,44,69],"ordered":[4],"field":[5,38],"of":[6,47,53],"real":[7,37],"numbers":[8],"with":[9,61],"restricted":[10,48],"$\\mathbb{R}_{\\mathscr{H}}$-definable":[11],"analytic":[12],"functions":[13,42,55],"admits":[14],"quantifier":[15],"elimination":[16],"if":[17],"we":[18,66],"add":[19],"a":[20],"function":[21,26],"symbol":[22],"$^{-1}$":[23],"for":[24],"$x\\mapsto":[27],"\\frac{1}{x}$":[28],"(with":[29],"$0^{-1}=0$":[30],"by":[31,40],"convention),":[32],"where":[33],"$\\mathbb{R}_{\\mathscr{H}}$":[34],"is":[35,73],"augmented":[39],"in":[43],"family":[45],"$\\mathscr{H}$":[46,65],"parts":[49],"(real":[50],"and":[51],"imaginary)":[52],"holomorphic":[54],"which":[56],"satisfies":[57],"certain":[58],"conditions.":[59],"Further,":[60],"another":[62],"condition":[63],"on":[64],"structure":[70],"($\\mathbb{R}_{\\mathscr{H}}$,":[71],"constants)":[72],"strongly":[74],"model":[75],"complete.":[76]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2059214986","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2024-12-11T13:46:59.248925","created_date":"2016-06-24"}