{"id":"https://openalex.org/W2036069135","doi":"https://doi.org/10.2178/jsl/1294170994","title":"On the jump classes of noncuppable enumeration degrees","display_name":"On the jump classes of noncuppable enumeration degrees","publication_year":2011,"publication_date":"2011-01-04","ids":{"openalex":"https://openalex.org/W2036069135","doi":"https://doi.org/10.2178/jsl/1294170994","mag":"2036069135"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1294170994","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1294170994","pdf_url":null,"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":"The Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082044410","display_name":"Charles M. Harris","orcid":null},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Charles M. Harris","raw_affiliation_strings":["University of Leeds, Department of Mathematics, Leeds, UK, E-mail:","School of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Leeds, Department of Mathematics, Leeds, UK, E-mail:","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"School of Mathematics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5082044410"],"corresponding_institution_ids":["https://openalex.org/I130828816"],"apc_list":null,"apc_paid":null,"fwci":0.299,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.59461173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"76","issue":"1","first_page":"177","last_page":"197"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":1.0,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":1.0,"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/T11567","display_name":"semigroups and automata theory","score":0.9930999875068665,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9904000163078308,"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/enumeration","display_name":"Enumeration","score":0.9358179569244385},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.8436316251754761},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7102375030517578},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6934032440185547},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6850920915603638},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6694412231445312},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5346758961677551},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.4195420444011688},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4070511758327484},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32967323064804077},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17943966388702393},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11843147873878479},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.040624141693115234},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.03805357217788696}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.9358179569244385},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.8436316251754761},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7102375030517578},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6934032440185547},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6850920915603638},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6694412231445312},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5346758961677551},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.4195420444011688},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4070511758327484},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32967323064804077},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17943966388702393},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11843147873878479},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.040624141693115234},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.03805357217788696},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2178/jsl/1294170994","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1294170994","pdf_url":null,"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":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/02b34819-cee7-4e82-8ef9-60db2a83c26a","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/02b34819-cee7-4e82-8ef9-60db2a83c26a","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Harris, C M 2011, 'On the jump classes of noncuppable enumeration degrees', Journal of Symbolic Logic, vol. 76, no. 1, pp. 177-197. < http://www.scopus.com/inward/record.url?eid=2-s2.0-79953225892&partnerID=40&md5=d0e0cd01d38490f677d1a8c915d67c96 >","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.528.3715","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.528.3715","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www1.maths.leeds.ac.uk/~charlie/papers/pdfversions/nonCupping.pdf","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1294170994","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1294170994","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6656001343","display_name":null,"funder_award_id":"EP/G000212/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W334685031","https://openalex.org/W352853685","https://openalex.org/W623765668","https://openalex.org/W1972685794","https://openalex.org/W1989929787","https://openalex.org/W2011693882","https://openalex.org/W2013740965","https://openalex.org/W2018499782","https://openalex.org/W2021872519","https://openalex.org/W2037662783","https://openalex.org/W2055180636","https://openalex.org/W2056414301","https://openalex.org/W2068438761","https://openalex.org/W2126750620","https://openalex.org/W2147472592","https://openalex.org/W2616606085","https://openalex.org/W4232277851","https://openalex.org/W6653534608"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2406961474","https://openalex.org/W2143566611","https://openalex.org/W2013740965","https://openalex.org/W588267724","https://openalex.org/W4297743441","https://openalex.org/W2952598754","https://openalex.org/W2026779193"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"prove":[2],"that":[3,25,55],"for":[4],"every":[5,65],"\u03a3":[6,16,58],"2":[7,17,59],"0":[8,18,22,60],"enumeration":[9,62],"degree":[10,19],"b":[11],"there":[12,56],"exists":[13],"a":[14,20],"noncuppable":[15,61],"&gt;":[21],"e":[23],"such":[24],"and":[26,45],".":[27,80],"This":[28],"allows":[29],"us":[30],"to":[31],"deduce,":[32],"from":[33],"results":[34],"on":[35],"the":[36,41,46,51,72,77],"high/low":[37,73],"jump":[38,47,74],"hierarchy":[39,75],"in":[40,76],"local":[42],"Turing":[43],"degrees":[44,63],"preserving":[48],"properties":[49],"of":[50,71,79],"standard":[52],"embedding":[53],",":[54],"exist":[57],"at":[64],"possible\u2014i.e.,":[66],"above":[67],"low":[68],"1":[69],"\u2014level":[70],"context":[78]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}