{"id":"https://openalex.org/W4415882576","doi":"https://doi.org/10.1007/s00153-025-00996-z","title":"Nonvanishing derived limits without scales","display_name":"Nonvanishing derived limits without scales","publication_year":2025,"publication_date":"2025-11-04","ids":{"openalex":"https://openalex.org/W4415882576","doi":"https://doi.org/10.1007/s00153-025-00996-z","pmid":"https://pubmed.ncbi.nlm.nih.gov/41657970"},"language":"en","primary_location":{"id":"doi:10.1007/s00153-025-00996-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-025-00996-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-025-00996-z.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00153-025-00996-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5098821155","display_name":"Matteo Casarosa","orcid":null},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["FR","IT"],"is_corresponding":true,"raw_author_name":"Matteo Casarosa","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy","Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (IMJ-PRG), Universit\u00e9 Paris Cit\u00e9, B\u00e2timent Sophie Germain, 8 Place Aur\u00e9lie Nemours, 75013 Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]},{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (IMJ-PRG), Universit\u00e9 Paris Cit\u00e9, B\u00e2timent Sophie Germain, 8 Place Aur\u00e9lie Nemours, 75013 Paris, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I3017942884"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5098821155"],"corresponding_institution_ids":["https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I9360294"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3667241,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"2","first_page":"177","last_page":"191"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.5285999774932861,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.5285999774932861,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.16750000417232513,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.029999999329447746,"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/functor","display_name":"Functor","score":0.7063000202178955},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5864999890327454},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5656999945640564},{"id":"https://openalex.org/keywords/inverse-limit","display_name":"Inverse limit","score":0.5652999877929688},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5192999839782715},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.48980000615119934},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4178999960422516},{"id":"https://openalex.org/keywords/additive-function","display_name":"Additive function","score":0.3984000086784363}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9218000173568726},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.7063000202178955},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5864999890327454},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5656999945640564},{"id":"https://openalex.org/C53936288","wikidata":"https://www.wikidata.org/wiki/Q2634828","display_name":"Inverse limit","level":2,"score":0.5652999877929688},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5343999862670898},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5192999839782715},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.48980000615119934},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4178999960422516},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.3984000086784363},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3824999928474426},{"id":"https://openalex.org/C122129529","wikidata":"https://www.wikidata.org/wiki/Q2634828","display_name":"Inverse system","level":3,"score":0.33169999718666077},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.3172000050544739},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3109999895095825},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C186921422","wikidata":"https://www.wikidata.org/wiki/Q318737","display_name":"Abelian category","level":3,"score":0.28859999775886536},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00153-025-00996-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-025-00996-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-025-00996-z.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},{"id":"pmid:41657970","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41657970","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for mathematical logic","raw_type":null},{"id":"pmh:oai:europepmc.org:11688728","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12881080","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s00153-025-00996-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-025-00996-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-025-00996-z.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G851281336","display_name":"Compactness in set theory, with applications to algebra and graph theory","funder_award_id":"GA23-04683S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G907191879","display_name":null,"funder_award_id":"101077154","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320322482","display_name":"Akademie V\u011bd \u010cesk\u00e9 Republiky","ror":"https://ror.org/053avzc18"},{"id":"https://openalex.org/F4320323428","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57"},{"id":"https://openalex.org/F4320328290","display_name":"Fondation Sciences Math\u00e9matiques de Paris","ror":null},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415882576.pdf","grobid_xml":"https://content.openalex.org/works/W4415882576.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1820243991","https://openalex.org/W1969030255","https://openalex.org/W1991721857","https://openalex.org/W2041590141","https://openalex.org/W2091746243","https://openalex.org/W2094286713","https://openalex.org/W2332334926","https://openalex.org/W2963907882","https://openalex.org/W3082806616","https://openalex.org/W4241853888","https://openalex.org/W4243208804","https://openalex.org/W4283025149"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"The":[1],"derived":[2,85,158],"functors":[3],"$$\\lim":[4],"^n$$":[5],"<mml:math":[6,55,67,89,112,140,185],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[7,56,68,90,113,141,186],"<mml:msup>":[8,123],"<mml:mo>lim</mml:mo>":[9],"<mml:mi>n</mml:mi>":[10],"</mml:msup>":[11,126],"</mml:math>":[12,58,77,92,129,147,202],"of":[13,32,50,59,87,98,106,164,172,212],"the":[14,30,48,51,96,162],"inverse":[15,52],"limit":[16],"are":[17,26,167],"widely":[18],"studied":[19],"for":[20,45,83],"their":[21],"topological":[22],"applications,":[23],"among":[24],"which":[25],"some":[27],"repercussions":[28],"on":[29],"additivity":[31],"strong":[33,165],"homology.":[34],"Set":[35],"theory":[36],"has":[37],"proven":[38],"useful":[39],"in":[40,47],"dealing":[41],"with":[42,169],"these":[43],"functors,":[44],"instance":[46],"case":[49],"system":[53],"$$\\textbf{A}$$":[54,88],"<mml:mi>A</mml:mi>":[57,91],"abelian":[60],"groups":[61],"indexed":[62],"over":[63],"$${}^\\omega":[64],"\\omega":[65,108],"$$":[66,139,184],"<mml:mrow>":[69,114,142,187],"<mml:mmultiscripts>":[70,116],"<mml:mrow/>":[71,72,117,118],"<mml:mi>\u03c9</mml:mi>":[73,75,119,121,199],"</mml:mmultiscripts>":[74,120],"</mml:mrow>":[76,128,146,201],".":[78],"So":[79],"far,":[80],"consistency":[81],"results":[82],"nonvanishing":[84,157],"limits":[86],"have":[93],"always":[94],"assumed":[95],"existence":[97],"a":[99,102,206,210],"scale":[100],"(i.e.":[101],"linear":[103],"cofinal":[104],"subset":[105],"$$({}^\\omega":[107],",":[109,130,203],"\\le":[110,175,178],"^*)$$":[111],"<mml:mo>(</mml:mo>":[115],"<mml:mo>,</mml:mo>":[122],"<mml:mo>\u2264</mml:mo>":[124,192,194],"<mml:mo>\u2217</mml:mo>":[125],"<mml:mo>)</mml:mo>":[127],"or":[131],"equivalently":[132],"that":[133,152,156],"$$\\mathfrak":[134],"{b}":[135,177],"=":[136],"\\mathfrak":[137,176,179],"{d}":[138,180],"<mml:mi>b</mml:mi>":[143,193],"<mml:mo>=</mml:mo>":[144],"<mml:mi>d</mml:mi>":[145,195],").":[148],"Here":[149],"we":[150],"eliminate":[151],"assumption":[153],"and":[154,160],"prove":[155],"limits,":[159],"hence":[161],"non-additivity":[163],"homology,":[166],"consistent":[168],"any":[170],"value":[171],"$$\\aleph":[173],"_1":[174],"&lt;":[181],"\\aleph":[182],"_\\omega":[183],"<mml:msub>":[188,197],"<mml:mi>\u2135</mml:mi>":[189,198],"<mml:mn>1</mml:mn>":[190],"</mml:msub>":[191,200],"<mml:mo>&lt;</mml:mo>":[196],"thus":[204],"giving":[205],"partial":[207],"answer":[208],"to":[209],"question":[211],"Bannister.":[213]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-11-04T00:00:00"}