{"id":"https://openalex.org/W4416245836","doi":"https://doi.org/10.1007/s00153-025-00991-4","title":"On sequential theorems in Reverse Mathematics","display_name":"On sequential theorems in Reverse Mathematics","publication_year":2025,"publication_date":"2025-11-15","ids":{"openalex":"https://openalex.org/W4416245836","doi":"https://doi.org/10.1007/s00153-025-00991-4"},"language":"en","primary_location":{"id":"doi:10.1007/s00153-025-00991-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-025-00991-4","pdf_url":null,"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"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s00153-025-00991-4","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113576097","display_name":"Dag Normann","orcid":null},"institutions":[{"id":"https://openalex.org/I184942183","display_name":"University of Oslo","ror":"https://ror.org/01xtthb56","country_code":"NO","type":"education","lineage":["https://openalex.org/I184942183"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Dag Normann","raw_affiliation_strings":["Department of Mathematics, The University of Oslo, P.O. Box 1053, Blindern, Oslo, N-0316, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Oslo, P.O. Box 1053, Blindern, Oslo, N-0316, Norway","institution_ids":["https://openalex.org/I184942183"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073669576","display_name":"Sam Sanders","orcid":"https://orcid.org/0000-0001-8256-0009"},"institutions":[{"id":"https://openalex.org/I2799784675","display_name":"University Hospitals of the Ruhr-University of Bochum","ror":"https://ror.org/03zcpvf19","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I2799784675"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sam Sanders","raw_affiliation_strings":["Department of Philosophy II, RUB Bochum, Bochum, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Philosophy II, RUB Bochum, Bochum, Germany","institution_ids":["https://openalex.org/I2799784675"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073669576"],"corresponding_institution_ids":["https://openalex.org/I2799784675"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29152424,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"2","first_page":"275","last_page":"295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.27300000190734863,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.27300000190734863,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.11810000240802765,"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/T10126","display_name":"Logic, programming, and type systems","score":0.11590000241994858,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6480000019073486},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6359000205993652},{"id":"https://openalex.org/keywords/reverse-mathematics","display_name":"Reverse mathematics","score":0.6151000261306763},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5284000039100647},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.421999990940094},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.34310001134872437},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.33570000529289246}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.809499979019165},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6480000019073486},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6359000205993652},{"id":"https://openalex.org/C127753061","wikidata":"https://www.wikidata.org/wiki/Q2005236","display_name":"Reverse mathematics","level":3,"score":0.6151000261306763},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5284000039100647},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4544000029563904},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.421999990940094},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.33570000529289246},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.32919999957084656},{"id":"https://openalex.org/C47884741","wikidata":"https://www.wikidata.org/wiki/Q1166618","display_name":"Mathematical logic","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C185701065","wikidata":"https://www.wikidata.org/wiki/Q159943","display_name":"Abstract algebra","level":3,"score":0.2734000086784363},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.26570001244544983},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.2612999975681305}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00153-025-00991-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-025-00991-4","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.1007/s00153-025-00991-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-025-00991-4","pdf_url":null,"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/G1568257504","display_name":null,"funder_award_id":"Projekt KT43","funder_id":"https://openalex.org/F4320324316","funder_display_name":"Klaus Tschira Stiftung"}],"funders":[{"id":"https://openalex.org/F4320324316","display_name":"Klaus Tschira Stiftung","ror":"https://ror.org/052jep661"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W175594167","https://openalex.org/W1507744378","https://openalex.org/W1545464436","https://openalex.org/W1590304156","https://openalex.org/W1938681473","https://openalex.org/W1974355866","https://openalex.org/W1984505680","https://openalex.org/W2004000165","https://openalex.org/W2013915186","https://openalex.org/W2028509288","https://openalex.org/W2044762117","https://openalex.org/W2060740478","https://openalex.org/W2081624356","https://openalex.org/W2089230867","https://openalex.org/W2089902858","https://openalex.org/W2134101218","https://openalex.org/W2249336712","https://openalex.org/W2293460502","https://openalex.org/W2603470071","https://openalex.org/W2769377332","https://openalex.org/W2811046655","https://openalex.org/W2963693343","https://openalex.org/W3005683397","https://openalex.org/W3006582179","https://openalex.org/W3090093830","https://openalex.org/W3090687855","https://openalex.org/W3119916969","https://openalex.org/W4226517410","https://openalex.org/W4287313091","https://openalex.org/W4300961286","https://openalex.org/W4362731161","https://openalex.org/W4382560505","https://openalex.org/W4386423060","https://openalex.org/W4387696120","https://openalex.org/W4402548675","https://openalex.org/W4404721081"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Many":[1],"theorems":[2,84],"of":[3,35,41,75,85,109],"mathematics":[4],"have":[5,60,97],"the":[6,53,61,73,94,106,110,124,141],"form":[7],"that":[8,31,93],"for":[9,32],"a":[10,15,23,33,39],"certain":[11],"problem":[12],",":[13],"e.g.":[14,88],"differential":[16],"equation":[17],"or":[18],"polynomial":[19],"(in)equality,":[20],"there":[21,37],"exists":[22],"solution":[24],".":[25,147],"The":[26,43],"sequential":[27,46,95],"version":[28],"then":[29],"states":[30],"sequence":[34,40],"problems,":[36],"is":[38,70,133,137],"solutions.":[42],"original":[44,111],"and":[45,58,115,136],"theorem":[47],"can":[48],"often":[49,59],"be":[50],"proved":[51],"via":[52],"same":[54,62],"(or":[55,63],"similar)":[56,64],"proof":[57],"logical":[65,100],"properties,":[66],"esp.":[67],"if":[68],"everything":[69],"formulated":[71],"in":[72,129],"language":[74],"second-order":[76],"arithmetic.":[77],"In":[78,102],"this":[79],"paper,":[80],"we":[81],"identify":[82],"basic":[83],"third-order":[86],"arithmetic,":[87],"concerning":[89],"semi-continuous":[90],"functions,":[91],"such":[92],"versions":[96],"very":[98,113],"different":[99,114],"properties.":[101],"particular,":[103],"depending":[104],"on":[105,143],"constructive":[107],"status":[108],"theorem,":[112],"independent":[116],"choice":[117],"principles":[118],"are":[119],"needed.":[120],"Despite":[121],"these":[122],"differences,":[123],"associated":[125],"Reverse":[126],"Mathematics,":[127],"working":[128],"Kohlenbach\u2019s":[130],"higher-order":[131],"framework,":[132],"rather":[134],"elegant":[135],"still":[138],"based":[139],"at":[140],"core":[142],"weak":[144],"K\u00f6nig\u2019s":[145],"lemma":[146]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-11-15T00:00:00"}