{"id":"https://openalex.org/W2141032297","doi":"https://doi.org/10.1142/s0219061303000224","title":"EXPANSIONS OF ALGEBRAICALLY CLOSED FIELDS II: FUNCTIONS OF SEVERAL VARIABLES","display_name":"EXPANSIONS OF ALGEBRAICALLY CLOSED FIELDS II: FUNCTIONS OF SEVERAL VARIABLES","publication_year":2003,"publication_date":"2003-05-01","ids":{"openalex":"https://openalex.org/W2141032297","doi":"https://doi.org/10.1142/s0219061303000224","mag":"2141032297"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061303000224","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061303000224","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical 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/A5047276331","display_name":"Ya\u2019acov Peterzil","orcid":null},"institutions":[{"id":"https://openalex.org/I91203450","display_name":"University of Haifa","ror":"https://ror.org/02f009v59","country_code":"IL","type":"education","lineage":["https://openalex.org/I91203450"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"YA'ACOV PETERZIL","raw_affiliation_strings":["Department of Mathematics, University of Haifa, Haifa, Israel","Department of Mathematics, University of Haifa, Haifa, ISRAEL"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Haifa, Haifa, Israel","institution_ids":["https://openalex.org/I91203450"]},{"raw_affiliation_string":"Department of Mathematics, University of Haifa, Haifa, ISRAEL","institution_ids":["https://openalex.org/I91203450"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005424226","display_name":"Sergei Starchenko","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"SERGEI STARCHENKO","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8697,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.73332548,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"03","issue":"01","first_page":"1","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9994000196456909,"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":0.9994000196456909,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9990000128746033,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9980999827384949,"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/meromorphic-function","display_name":"Meromorphic function","score":0.9190210103988647},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8431007862091064},{"id":"https://openalex.org/keywords/algebraically-closed-field","display_name":"Algebraically closed field","score":0.8210917711257935},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6954188346862793},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6662656664848328},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.6135956645011902},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.6013368368148804},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5708307027816772},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5134290456771851},{"id":"https://openalex.org/keywords/analytic-function","display_name":"Analytic function","score":0.5003316402435303},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4001011848449707},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32587096095085144},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20979014039039612}],"concepts":[{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.9190210103988647},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8431007862091064},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.8210917711257935},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6954188346862793},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6662656664848328},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6135956645011902},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.6013368368148804},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5708307027816772},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5134290456771851},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.5003316402435303},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4001011848449707},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32587096095085144},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20979014039039612},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219061303000224","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061303000224","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1486898453","https://openalex.org/W1958493481","https://openalex.org/W2079116828","https://openalex.org/W2144033225","https://openalex.org/W2162052349","https://openalex.org/W2314912482","https://openalex.org/W4231864194","https://openalex.org/W4233761642","https://openalex.org/W4236562666","https://openalex.org/W4297913868","https://openalex.org/W4388372514"],"related_works":["https://openalex.org/W2033053344","https://openalex.org/W2167154330","https://openalex.org/W3106133691","https://openalex.org/W2439115288","https://openalex.org/W2021915098","https://openalex.org/W3103780039","https://openalex.org/W3026358768","https://openalex.org/W2141032297","https://openalex.org/W2963586505","https://openalex.org/W2166957267"],"abstract_inverted_index":{"Let":[0],"\u211b":[1],"be":[2],"an":[3],"o-minimal":[4],"expansion":[5],"of":[6,21,38,44,56,94,114],"a":[7,86],"real":[8],"closed":[9,28],"field":[10,29],"R.":[11],"We":[12,33,66,89],"continue":[13],"here":[14],"the":[15,26,35,57,102],"investigation":[16],"we":[17],"began":[18],"in":[19,117],"[11]":[20],"differentiability":[22],"with":[23,98],"respect":[24],"to":[25,101],"algebraically":[27],"[Formula:":[30],"see":[31],"text].":[32],"develop":[34],"basic":[36],"theory":[37],"such":[39],"K-differentiability":[40],"for":[41,63],"definable":[42,64,76,92],"functions":[43,71],"several":[45],"variables,":[46],"proving":[47],"theorems":[48,62],"on":[49,81,106],"removable":[50],"singularities":[51],"as":[52,54],"well":[53],"analogues":[55,93],"Weierstrass":[58],"preparation":[59],"and":[60,72,110],"division":[61],"functions.":[65],"consider":[67],"also":[68],"definably":[69],"meromorphic":[70,80],"prove":[73],"that":[74],"every":[75],"function":[77],"which":[78],"is":[79,84],"K":[82],"n":[83],"necessarily":[85],"rational":[87],"function.":[88],"finally":[90],"discuss":[91],"complex":[95,108],"analytic":[96],"manifolds,":[97,109],"possible":[99],"connections":[100],"model":[103],"theoretic":[104],"work":[105],"compact":[107],"present":[111],"two":[112],"examples":[113],"\"nonstandard":[115],"manifolds\"":[116],"our":[118],"setting.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
