{"id":"https://openalex.org/W3160890305","doi":"https://doi.org/10.1007/s00153-022-00851-5","title":"Bachmann\u2013Howard derivatives","display_name":"Bachmann\u2013Howard derivatives","publication_year":2022,"publication_date":"2022-10-26","ids":{"openalex":"https://openalex.org/W3160890305","doi":"https://doi.org/10.1007/s00153-022-00851-5","mag":"3160890305"},"language":"en","primary_location":{"id":"doi:10.1007/s00153-022-00851-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-022-00851-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-022-00851-5.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","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://link.springer.com/content/pdf/10.1007/s00153-022-00851-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071872554","display_name":"Anton Freund","orcid":"https://orcid.org/0000-0002-5456-5790"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Anton Freund","raw_affiliation_strings":["Fachbereich Mathematik, Technische Universit\u00e4t Darmstadt, Schlossgartenstr.\u00a07, 64289, Darmstadt, Germany"],"raw_orcid":"https://orcid.org/0000-0002-5456-5790","affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, Technische Universit\u00e4t Darmstadt, Schlossgartenstr.\u00a07, 64289, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071872554"],"corresponding_institution_ids":["https://openalex.org/I31512782"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.4525,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63094935,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"62","issue":"5-6","first_page":"581","last_page":"618"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9940999746322632,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9940999746322632,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9939000010490417,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9922000169754028,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.8986389636993408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8424171209335327},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.8009072542190552},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5079386830329895},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.4946005046367645},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4893895983695984},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4735138714313507},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3748626708984375},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3457293212413788},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30631768703460693},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09746110439300537},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.09730574488639832}],"concepts":[{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.8986389636993408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8424171209335327},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.8009072542190552},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5079386830329895},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.4946005046367645},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4893895983695984},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4735138714313507},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3748626708984375},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3457293212413788},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30631768703460693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09746110439300537},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.09730574488639832},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00153-022-00851-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-022-00851-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-022-00851-5.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:153150","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/view/person/Freund=3AAnton=3A=3A.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"}],"best_oa_location":{"id":"doi:10.1007/s00153-022-00851-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-022-00851-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-022-00851-5.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","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/G3852438965","display_name":null,"funder_award_id":"460597863","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3160890305.pdf","grobid_xml":"https://content.openalex.org/works/W3160890305.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W6616102","https://openalex.org/W1512244371","https://openalex.org/W1576077894","https://openalex.org/W1980969069","https://openalex.org/W1988230691","https://openalex.org/W1994073383","https://openalex.org/W2018765574","https://openalex.org/W2024982091","https://openalex.org/W2030880007","https://openalex.org/W2052953762","https://openalex.org/W2076508310","https://openalex.org/W2082844458","https://openalex.org/W2115072159","https://openalex.org/W2163841074","https://openalex.org/W2243196114","https://openalex.org/W2890902398","https://openalex.org/W2891240794","https://openalex.org/W2891361014","https://openalex.org/W2912538988","https://openalex.org/W2952241302","https://openalex.org/W2963030916","https://openalex.org/W2995344442","https://openalex.org/W2999820809","https://openalex.org/W3102088491","https://openalex.org/W3128609693","https://openalex.org/W4229690001"],"related_works":["https://openalex.org/W2888918612","https://openalex.org/W2166285859","https://openalex.org/W3148597776","https://openalex.org/W2060412688","https://openalex.org/W1538206641","https://openalex.org/W3211656382","https://openalex.org/W2025370853","https://openalex.org/W4235940179","https://openalex.org/W1972183506","https://openalex.org/W3142104043"],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,10,23,73,113,127],"generally":[3],"accepted":[4],"that":[5,38,55,80,126,157],"H.":[6],"Friedman\u2019s":[7],"gap":[8,40,98,143],"condition":[9,41,99,144],"closely":[11],"related":[12],"to":[13,122,129,160],"iterated":[14],"collapsing":[15,64],"functions":[16],"from":[17,43],"ordinal":[18,109],"analysis.":[19],"But":[20],"what":[21],"precisely":[22],"the":[24,28,39,56,70,86,92,97,130,142],"connection?":[25],"We":[26,154],"offer":[27],"following":[29],"answer:":[30],"In":[31,85],"a":[32,77,124],"previous":[33],"paper":[34],"we":[35,53,81,89],"have":[36],"shown":[37,134],"arises":[42],"an":[44,74],"iterative":[45],"construction":[46,58,79],"on":[47,91,96,107,145],"transformations":[48],"of":[49,76,164],"partial":[50],"orders.":[51],"Here":[52],"show":[54],"parallel":[57],"for":[59,100,115],"linear":[60,71],"orders":[61],"yields":[62],"familiar":[63],"functions.":[65],"The":[66],"iteration":[67],"step":[68],"in":[69],"case":[72],"instance":[75],"general":[78],"call":[82],"\u2018Bachmann\u2013Howard":[83],"derivative\u2019.":[84],"present":[87],"paper,":[88],"focus":[90],"unary":[93,131],"case,":[94],"i.e.,":[95],"sequences":[101,146],"rather":[102,151],"than":[103],"trees":[104],"and,":[105],"correspondingly,":[106],"addition-free":[108],"notation":[110],"systems.":[111],"This":[112],"partly":[114],"convenience,":[116],"but":[117],"it":[118],"also":[119],"allows":[120],"us":[121],"clarify":[123],"phenomenon":[125],"specific":[128],"setting:":[132],"As":[133],"by":[135],"van":[136],"der":[137],"Meeren,":[138],"Rathjen":[139],"and":[140],"Weiermann,":[141],"admits":[147],"two":[148],"linearizations":[149],"with":[150],"different":[152,161],"properties.":[153],"will":[155],"see":[156],"these":[158],"correspond":[159],"recursive":[162],"constructions":[163],"sequences.":[165]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
