{"id":"https://openalex.org/W2065827458","doi":"https://doi.org/10.2307/2273375","title":"Splitting theorems for speed-up related to order of enumeration","display_name":"Splitting theorems for speed-up related to order of enumeration","publication_year":1982,"publication_date":"1982-03-01","ids":{"openalex":"https://openalex.org/W2065827458","doi":"https://doi.org/10.2307/2273375","mag":"2065827458"},"language":"en","primary_location":{"id":"doi:10.2307/2273375","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273375","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":"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/A5035882360","display_name":"Adam Dawes","orcid":null},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"A. M. Dawes","raw_affiliation_strings":["University of Western Ontario, London, CanadaN6A5B9"],"affiliations":[{"raw_affiliation_string":"University of Western Ontario, London, CanadaN6A5B9","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035882360"],"corresponding_institution_ids":["https://openalex.org/I125749732"],"apc_list":null,"apc_paid":null,"fwci":0.5497,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66289071,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"47","issue":"1","first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9990000128746033,"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":0.9990000128746033,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9855999946594238,"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/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.9639225602149963},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.9397780299186707},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.902611494064331},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6381361484527588},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.6336586475372314},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6191778779029846},{"id":"https://openalex.org/keywords/maximal-set","display_name":"Maximal set","score":0.6023306846618652},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5942249894142151},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.58321213722229},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5728604793548584},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5064326524734497},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4009823203086853},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2793755531311035},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06293991208076477}],"concepts":[{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.9639225602149963},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.9397780299186707},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.902611494064331},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6381361484527588},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.6336586475372314},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6191778779029846},{"id":"https://openalex.org/C188521023","wikidata":"https://www.wikidata.org/wiki/Q6795644","display_name":"Maximal set","level":3,"score":0.6023306846618652},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5942249894142151},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.58321213722229},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5728604793548584},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5064326524734497},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4009823203086853},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2793755531311035},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06293991208076477},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273375","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273375","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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183740934","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183740934","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W2017282012","https://openalex.org/W2020242021","https://openalex.org/W2044539289","https://openalex.org/W2081200353","https://openalex.org/W2089442854","https://openalex.org/W2117832390","https://openalex.org/W2530006810","https://openalex.org/W2905135108"],"related_works":["https://openalex.org/W2037833610","https://openalex.org/W1973052363","https://openalex.org/W2065827458","https://openalex.org/W2140758900","https://openalex.org/W2332645982","https://openalex.org/W4249600134","https://openalex.org/W17676366","https://openalex.org/W253059699","https://openalex.org/W1980641386","https://openalex.org/W2142539551"],"abstract_inverted_index":{"Abstract":[0],"It":[1,37],"is":[2,38,79],"known":[3],"from":[4],"work":[5],"of":[6,49,67,89],"P.":[7],"Young":[8],"that":[9,23,40,80],"there":[10,24,81],"are":[11,25,44,82],"recursively":[12,50,57],"enumerable":[13,51,58],"sets":[14,26,65,84],"which":[15,27,68],"have":[16,30],"optimal":[17,87],"orders":[18,32],"for":[19],"enumeration,":[20],"and":[21],"also":[22],"fail":[28],"to":[29,76],"such":[31],"in":[33,46],"a":[34],"strong":[35],"sense.":[36],"shown":[39],"both":[41],"these":[42],"properties":[43],"widespread":[45],"the":[47,70],"class":[48],"sets.":[52],"In":[53],"fact,":[54],"any":[55],"infinite":[56],"set":[59],"can":[60],"be":[61],"split":[62],"into":[63],"two":[64],"each":[66],"has":[69],"property":[71],"under":[72],"consideration.":[73],"A":[74],"corollary":[75],"this":[77],"result":[78],"recursive":[83],"with":[85],"no":[86],"order":[88],"enumeration.":[90]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
