{"id":"https://openalex.org/W2072696085","doi":"https://doi.org/10.2307/2586760","title":"Infinitary properties of valued and ordered vector spaces","display_name":"Infinitary properties of valued and ordered vector spaces","publication_year":1999,"publication_date":"1999-03-01","ids":{"openalex":"https://openalex.org/W2072696085","doi":"https://doi.org/10.2307/2586760","mag":"2072696085"},"language":"en","primary_location":{"id":"doi:10.2307/2586760","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2586760","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/010C97824160948B08987F01B7CF3342/S0022481200013992a.pdf/div-class-title-infinitary-properties-of-valued-and-ordered-vector-spaces-div.pdf","source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/010C97824160948B08987F01B7CF3342/S0022481200013992a.pdf/div-class-title-infinitary-properties-of-valued-and-ordered-vector-spaces-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036218392","display_name":"Salma Kuhlmann","orcid":null},"institutions":[{"id":"https://openalex.org/I9267121","display_name":"Fields Institute for Research in Mathematical Sciences","ror":"https://ror.org/03zzj3f20","country_code":"CA","type":"facility","lineage":["https://openalex.org/I185261750","https://openalex.org/I9267121"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Salma Kuhlmann","raw_affiliation_strings":["The Fields Institute, 222, College Street, Toronto, Ontario, CanadaM5T 3J1, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Fields Institute, 222, College Street, Toronto, Ontario, CanadaM5T 3J1, E-mail:","institution_ids":["https://openalex.org/I9267121"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5036218392"],"corresponding_institution_ids":["https://openalex.org/I9267121"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25248869,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"1","first_page":"216","last_page":"226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9979000091552734,"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"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9969000220298767,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9851999878883362,"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/abelian-group","display_name":"Abelian group","score":0.8358132839202881},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7743284702301025},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.6929813027381897},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46730753779411316},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.45576155185699463},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.44343918561935425},{"id":"https://openalex.org/keywords/ordered-vector-space","display_name":"Ordered vector space","score":0.43323245644569397},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4142250716686249},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3867955803871155},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32712799310684204},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08346855640411377}],"concepts":[{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8358132839202881},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7743284702301025},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.6929813027381897},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46730753779411316},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45576155185699463},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.44343918561935425},{"id":"https://openalex.org/C113837420","wikidata":"https://www.wikidata.org/wiki/Q1503340","display_name":"Ordered vector space","level":5,"score":0.43323245644569397},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4142250716686249},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3867955803871155},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32712799310684204},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08346855640411377},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C6183050","wikidata":"https://www.wikidata.org/wiki/Q3058180","display_name":"Interpolation space","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C55112680","wikidata":"https://www.wikidata.org/wiki/Q190549","display_name":"Functional analysis","level":3,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2307/2586760","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2586760","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/010C97824160948B08987F01B7CF3342/S0022481200013992a.pdf/div-class-title-infinitary-properties-of-valued-and-ordered-vector-spaces-div.pdf","source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745701","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745701","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:CiteSeerX.psu:10.1.1.986.6526","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.986.6526","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://kops.uni-konstanz.de/bitstream/handle/123456789/554/Infinitary_properties_1999.pdf%3Bjsessionid%3D5C3B8DBBF28E9F63567803DFA8A631A6?sequence%3D1","raw_type":"text"},{"id":"pmh:oai:kops.uni-konstanz.de:123456789/554","is_oa":false,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-91897","pdf_url":null,"source":{"id":"https://openalex.org/S4306401487","display_name":"KOPS (University of Konstanz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189712700","host_organization_name":"University of Konstanz","host_organization_lineage":["https://openalex.org/I189712700"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Journal of Symbolic Logic. 1999, 64(1), S. 216-226. Verf\u00fcgbar unter: doi: 10.2307/2586760","raw_type":"doc-type:Text"}],"best_oa_location":{"id":"doi:10.2307/2586760","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2586760","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/010C97824160948B08987F01B7CF3342/S0022481200013992a.pdf/div-class-title-infinitary-properties-of-valued-and-ordered-vector-spaces-div.pdf","source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2072696085.pdf","grobid_xml":"https://content.openalex.org/works/W2072696085.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1485211506","https://openalex.org/W1551313231","https://openalex.org/W1607081528","https://openalex.org/W1969228601","https://openalex.org/W1975557405","https://openalex.org/W1997423220","https://openalex.org/W2010757891","https://openalex.org/W2075922000","https://openalex.org/W2145171097","https://openalex.org/W2554842236","https://openalex.org/W4312723694","https://openalex.org/W4312923885"],"related_works":["https://openalex.org/W2204201083","https://openalex.org/W2327962405","https://openalex.org/W2017525113","https://openalex.org/W2079030659","https://openalex.org/W2108615711","https://openalex.org/W3160949262","https://openalex.org/W2042334973","https://openalex.org/W2810928779","https://openalex.org/W4289764883","https://openalex.org/W115431596"],"abstract_inverted_index":{"\u00a71.":[0],"Introduction.":[1],"The":[2,145],"motivation":[3],"of":[4,27,43,50,77,93,148,155,188,213],"this":[5],"work":[6],"comes":[7],"from":[8],"two":[9,150],"different":[10],"directions:":[11],"infinite":[12],"abelian":[13,44,96,191],"groups,":[14],"and":[15],"ordered":[16,95,103,164],"algebraic":[17],"structures.":[18],"A":[19],"challenging":[20],"problem":[21],"in":[22,64,219],"both":[23],"cases":[24],"is":[25,34,142,158,204],"that":[26,40,49],"classification.":[28],"In":[29],"the":[30,41,58,75,83,91,120,125,136,149,178,182,198,220],"first":[31],"case,":[32,85],"it":[33,170],"known":[35],"for":[36,89,138],"example":[37],"(cf.":[38,133,222],"[KA])":[39],"classification":[42],"torsion":[45],"groups":[46],"amounts":[47],"to":[48,74,82,113],"reduced":[51,190],"p":[52,186,192,215],"-groups":[53],"by":[54,62,71,116],"numerical":[55,117],"invariants":[56,60,141],"called":[57],"Ulm":[59,63],"(given":[61],"[U]).":[65],"Ulm's":[66],"theorem":[67],"was":[68],"later":[69],"generalized":[70],"P.":[72],"Hill":[73],"class":[76,92],"totally":[78],"projective":[79],"groups.":[80,97],"As":[81],"second":[84],"let":[86],"us":[87],"consider":[88,169],"instance":[90],"divisible":[94],"These":[98],"may":[99],"be":[100],"viewed":[101],"as":[102,152,154,171],"\u211a-vector":[104],"spaces.":[105],"Their":[106],"theory":[107,126],"being":[108,123],"unstable,":[109],"we":[110],"cannot":[111],"hope":[112],"classify":[114],"them":[115],"invariants.":[118],"On":[119],"other":[121],"hand,":[122],"o-minimal,":[124],"enjoys":[127],"several":[128],"good":[129],"model":[130],"theoretic":[131],"properties":[132],"[P-S]),":[134],"so":[135],"search":[137],"some":[139],"reasonable":[140],"well":[143,153],"motivated.":[144],"common":[146],"denominator":[147],"cases,":[151],"many":[156],"others,":[157],"valuation":[159],"theory.":[160],"Indeed":[161],"given":[162],"an":[163],"vector":[165,174,207],"space,":[166,175],"one":[167],"can":[168],"a":[172,189,205],"valued":[173,206],"endowed":[176,196],"with":[177,197,217],"natural":[179],"valuation.":[180],"Also,":[181],"socle":[183],"G":[184,194,202],"[":[185],"]":[187],"-group":[193],",":[195,203],"height":[199],"function":[200],"h":[201],"space":[208],"over":[209],"(the":[210],"prime":[211],"field":[212],"characteristic":[214],")":[216],"values":[218],"ordinals":[221],"[F]).":[223]},"counts_by_year":[],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}
