{"id":"https://openalex.org/W2028556584","doi":"https://doi.org/10.2307/421047","title":"Geometry, Calculus and Zil'ber's Conjecture","display_name":"Geometry, Calculus and Zil'ber's Conjecture","publication_year":1996,"publication_date":"1996-03-01","ids":{"openalex":"https://openalex.org/W2028556584","doi":"https://doi.org/10.2307/421047","mag":"2028556584"},"language":"en","primary_location":{"id":"doi:10.2307/421047","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421047","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin of Symbolic 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 and Computer Science, Haifa University, Haifa, Israel.E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Haifa University, Haifa, Israel.E-mail:","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/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sergei Starchenko","raw_affiliation_strings":["Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA.E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA.E-mail:","institution_ids":["https://openalex.org/I200719446"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4901,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.61535876,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2","issue":"1","first_page":"72","last_page":"83"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number 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/T10061","display_name":"Algebraic Geometry and Number 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/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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9965000152587891,"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/mathematics","display_name":"Mathematics","score":0.7427552938461304},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.6167160272598267},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6110327243804932},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5990467667579651},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.45747753977775574},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4369598925113678},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.4346407949924469},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3681299388408661},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3165885806083679},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2842375338077545},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2391514778137207},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1464628279209137}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7427552938461304},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.6167160272598267},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6110327243804932},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5990467667579651},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.45747753977775574},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4369598925113678},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.4346407949924469},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3681299388408661},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3165885806083679},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2842375338077545},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2391514778137207},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1464628279209137}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/421047","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421047","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1182353422","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1182353422","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1522423813","https://openalex.org/W1822440022","https://openalex.org/W1976986198","https://openalex.org/W2010757891","https://openalex.org/W2050070395","https://openalex.org/W2063209841","https://openalex.org/W2066256748","https://openalex.org/W2070703446","https://openalex.org/W2130136812","https://openalex.org/W2146111369","https://openalex.org/W3205594860","https://openalex.org/W4233980873","https://openalex.org/W4237551483","https://openalex.org/W4254519827","https://openalex.org/W6631173518"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2949097972","https://openalex.org/W4299640900","https://openalex.org/W2141418112","https://openalex.org/W2738565459","https://openalex.org/W3163064202","https://openalex.org/W2348722996","https://openalex.org/W4230955177","https://openalex.org/W2608657692"],"abstract_inverted_index":{"\u00a71.":[0],"Introduction":[1],".":[2],"By":[3],"and":[4,18,55,105,128,133,157,181],"large,":[5],"definitions":[6],"of":[7,30,40,59,65,101,149,194,197,212],"a":[8,12,95,110,115,121,150,162,168],"differentiable":[9,116,159],"structure":[10,71,117,160],"on":[11,26],"set":[13,171],"involve":[14],"two":[15],"ingredients,":[16],"topology":[17,58],"algebra.":[19],"However,":[20],"in":[21,206],"some":[22,207],"cases,":[23],"partial":[24,103],"information":[25],"one":[27],"or":[28],"both":[29],"these":[31],"is":[32,38,72,82,120,124,148],"sufficient.":[33],"A":[34,98],"very":[35],"simple":[36],"example":[37,100],"that":[39],"the":[41,53,57,60,63,66,69,76,85,145,178,186,192],"field":[42,67],"\u211d":[43],"(or":[44],"any":[45],"real":[46],"closed":[47],"field)":[48],"where":[49],"algebra":[50],"alone":[51],"determines":[52,114],"ordering":[54],"hence":[56],"field:":[61],"In":[62],"case":[64],"\u2102,":[68],"algebraic":[70,104,156],"insufficient":[73],"to":[74,93],"determine":[75],"Euclidean":[77],"topology;":[78],"another":[79],"topology,":[80,180],"Zariski,":[81],"associated":[83],"with":[84,167,177,185],"ield":[86],"but":[87],"this":[88],"will":[89],"be":[90],"too":[91],"coarse":[92],"give":[94],"diferentiable":[96],"structure.":[97],"celebrated":[99],"how":[102],"topological":[106,163],"data":[107],"(":[108,118],"G":[109,119],"locally":[111],"euclidean":[112],"group)":[113,123],"Lie":[122],"Hilbert's":[125],"5th":[126],"problem":[127],"its":[129,182],"solution":[130],"by":[131],"Montgomery-Zippin":[132],"Gleason.":[134],"The":[135],"main":[136],"result":[137],"which":[138],"we":[139,153],"discuss":[140],"here":[141],"(see":[142],"[13]":[143],"for":[144],"full":[146],"version)":[147],"similar":[151],"flavor:":[152],"recover":[154],"an":[155],"later":[158],"from":[161],"data.":[164],"We":[165,189],"begin":[166],"linearly":[169],"ordered":[170],"\u27e8":[172,213],"M":[173,198,214],",":[174,200,215],"<\u27e9,":[175],"equipped":[176],"order":[179,209],"cartesian":[183],"products":[184],"product":[187],"topologies.":[188],"then":[190],"consider":[191],"collection":[193],"definable":[195],"subsets":[196],"n":[199,201],"=":[202],"1,":[203],"2,":[204],"\u2026,":[205],"first":[208],"expansion":[210],"\u2133":[211],"<\u27e9.":[216]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}