{"id":"https://openalex.org/W2036716130","doi":"https://doi.org/10.2168/lmcs-8(1:19)2012","title":"Derivation Lengths Classification of G\\\"odel's T Extending Howard's Assignment","display_name":"Derivation Lengths Classification of G\\\"odel's T Extending Howard's Assignment","publication_year":2012,"publication_date":"2012-03-06","ids":{"openalex":"https://openalex.org/W2036716130","doi":"https://doi.org/10.2168/lmcs-8(1:19)2012","mag":"2036716130"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-8(1:19)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(1:19)2012","pdf_url":"https://lmcs.episciences.org/1073/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/1073/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019535832","display_name":"Gunnar Wilken","orcid":"https://orcid.org/0000-0002-4019-9320"},"institutions":[{"id":"https://openalex.org/I142637625","display_name":"Okinawa Institute of Science and Technology Graduate University","ror":"https://ror.org/02qg15b79","country_code":"JP","type":"education","lineage":["https://openalex.org/I142637625"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Gunnar Wilken","raw_affiliation_strings":["Structural Cellular Biology Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-son, 904-0412 Okinawa, Japan","Okinawa Institute of Science and Technology, Mathematical Biology Unit, Japan"],"raw_orcid":"https://orcid.org/0000-0002-4019-9320","affiliations":[{"raw_affiliation_string":"Structural Cellular Biology Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-son, 904-0412 Okinawa, Japan","institution_ids":["https://openalex.org/I142637625"]},{"raw_affiliation_string":"Okinawa Institute of Science and Technology, Mathematical Biology Unit, Japan","institution_ids":["https://openalex.org/I142637625"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056618682","display_name":"Andreas Weiermann","orcid":"https://orcid.org/0000-0002-5561-5323"},"institutions":[{"id":"https://openalex.org/I2801227569","display_name":"Ghent University Hospital","ror":"https://ror.org/00xmkp704","country_code":"BE","type":"healthcare","lineage":["https://openalex.org/I2801227569"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Andreas Weiermann","raw_affiliation_strings":["Department of Mathematics, Ghent University, Building S22, Krijgslaan 281, B 9000 Gent, Bel-gium","Ghent University"],"raw_orcid":"https://orcid.org/0000-0002-5561-5323","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ghent University, Building S22, Krijgslaan 281, B 9000 Gent, Bel-gium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I2801227569"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019535832"],"corresponding_institution_ids":["https://openalex.org/I142637625"],"apc_list":null,"apc_paid":null,"fwci":0.4422,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.72462882,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"Volume 8, Issue 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.996999979019165,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.996999979019165,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9945999979972839,"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"}},{"id":"https://openalex.org/T10215","display_name":"Semantic Web and Ontologies","score":0.9740999937057495,"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/natural-number","display_name":"Natural number","score":0.7079267501831055},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6510279774665833},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.6415719389915466},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5905153751373291},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5505488514900208},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.532880961894989},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5044442415237427},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47928470373153687},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.47027498483657837},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4666250944137573},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45964622497558594},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45922794938087463},{"id":"https://openalex.org/keywords/finitary","display_name":"Finitary","score":0.45682764053344727},{"id":"https://openalex.org/keywords/combinatory-logic","display_name":"Combinatory logic","score":0.4519602060317993},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2370867133140564},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21427398920059204}],"concepts":[{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.7079267501831055},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6510279774665833},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6415719389915466},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5905153751373291},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5505488514900208},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.532880961894989},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5044442415237427},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47928470373153687},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.47027498483657837},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4666250944137573},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45964622497558594},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45922794938087463},{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.45682764053344727},{"id":"https://openalex.org/C79678938","wikidata":"https://www.wikidata.org/wiki/Q1481571","display_name":"Combinatory logic","level":2,"score":0.4519602060317993},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2370867133140564},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21427398920059204},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.2168/lmcs-8(1:19)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(1:19)2012","pdf_url":"https://lmcs.episciences.org/1073/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1203.0115","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1203.0115","pdf_url":"https://arxiv.org/pdf/1203.0115","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.754.4931","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.754.4931","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1203.0115.pdf","raw_type":"text"},{"id":"pmh:oai:archive.ugent.be:2062149","is_oa":true,"landing_page_url":"http://hdl.handle.net/1854/LU-2062149","pdf_url":null,"source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1860-5974","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:f4070cb0bec1453db8560f40fbbe8560","is_oa":true,"landing_page_url":"https://doaj.org/article/f4070cb0bec1453db8560f40fbbe8560","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 8, Issue 1 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-8(1:19)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(1:19)2012","pdf_url":"https://lmcs.episciences.org/1073/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2036716130.pdf","grobid_xml":"https://content.openalex.org/works/W2036716130.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W144641616","https://openalex.org/W1525064220","https://openalex.org/W1634878621","https://openalex.org/W1993440975","https://openalex.org/W1996792588","https://openalex.org/W2025478275","https://openalex.org/W2027585565","https://openalex.org/W2074448200","https://openalex.org/W2075296484","https://openalex.org/W2102009936","https://openalex.org/W2115737962","https://openalex.org/W2977904728","https://openalex.org/W3038873949","https://openalex.org/W3039529476","https://openalex.org/W4236364473"],"related_works":["https://openalex.org/W4288102793","https://openalex.org/W3098170724","https://openalex.org/W4206837156","https://openalex.org/W2975654559","https://openalex.org/W2359098868","https://openalex.org/W4388322088","https://openalex.org/W1981858926","https://openalex.org/W2125274893","https://openalex.org/W4297671843","https://openalex.org/W1492670229"],"abstract_inverted_index":{"Let":[0],"T":[1,36,93,99,120,172],"be":[2,70,157],"Goedel's":[3],"system":[4],"of":[5,9,33,35,40,83,98,119,144],"primitive":[6],"recursive":[7],"functionals":[8],"finite":[10],"type":[11],"in":[12,100,166],"the":[13,31,38,101,116,152],"lambda":[14,117,141],"formulation.":[15],"We":[16],"define":[17],"by":[18],"constructive":[19],"means":[20],"using":[21],"recursion":[22],"on":[23,87],"nested":[24],"multisets":[25],"a":[26,46,48,51,56,63,65,106,174],"multivalued":[27],"function":[28],"I":[29,84],"from":[30,138],"set":[32,39],"terms":[34,142],"into":[37],"natural":[41,57,66],"numbers":[42],"such":[43,74,177],"that":[44,75,151],"if":[45,55],"term":[47,52],"reduces":[49],"to":[50,62,72,133,159],"b":[53,73],"and":[54,94,121],"number":[58,67],"I(a)":[59,76],"is":[60,77,85,149,173],"assigned":[61,71],"then":[64],"I(b)":[68],"can":[69,156],"greater":[78],"than":[79],"I(b).":[80],"The":[81],"construction":[82],"based":[86],"Howard's":[88],"1970":[89],"ordinal":[90],"assignment":[91],"for":[92,115,176],"Weiermann's":[95,126],"1996":[96,127],"treatment":[97],"combinatory":[102,145],"logic":[103,146],"version.":[104],"As":[105],"corollary":[107],"we":[108],"obtain":[109],"an":[110],"optimal":[111],"derivation":[112],"length":[113],"classification":[114],"formulation":[118],"its":[122],"fragments.":[123],"Compared":[124],"with":[125,140],"exposition":[128],"this":[129],"article":[130],"yields":[131],"solutions":[132],"several":[134],"non-trivial":[135],"problems":[136],"arising":[137],"dealing":[139],"instead":[143],"terms.":[147],"It":[148],"expected":[150],"methods":[153],"developed":[154],"here":[155],"applied":[158],"other":[160],"higher":[161],"order":[162],"rewrite":[163],"systems":[164],"resulting":[165],"new":[167],"powerful":[168],"termination":[169],"orderings":[170],"since":[171],"paradigm":[175],"systems.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}