{"id":"https://openalex.org/W2022403147","doi":"https://doi.org/10.2307/2271945","title":"Controlling the dependence degree of a recursively enumerable vector space","display_name":"Controlling the dependence degree of a recursively enumerable vector space","publication_year":1978,"publication_date":"1978-03-01","ids":{"openalex":"https://openalex.org/W2022403147","doi":"https://doi.org/10.2307/2271945","mag":"2022403147"},"language":"en","primary_location":{"id":"doi:10.2307/2271945","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271945","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/A5041739806","display_name":"Richard A. Shore","orcid":"https://orcid.org/0000-0003-0381-5259"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Richard A. Shore","raw_affiliation_strings":["Cornell University, Ithaca, NY 14853"],"affiliations":[{"raw_affiliation_string":"Cornell University, Ithaca, NY 14853","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041739806"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":1.5921,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.82821332,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"43","issue":"1","first_page":"13","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9907000064849854,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9854000210762024,"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/computability-theory","display_name":"Computability theory","score":0.8419525623321533},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.6929474472999573},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.6888055801391602},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.5770508646965027},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5585087537765503},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5522430539131165},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.5418968200683594},{"id":"https://openalex.org/keywords/universal-algebra","display_name":"Universal algebra","score":0.45682716369628906},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4376319646835327},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4299778938293457},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.4147490859031677},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32577669620513916},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31969916820526123},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2909930944442749},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1916634440422058}],"concepts":[{"id":"https://openalex.org/C111142201","wikidata":"https://www.wikidata.org/wiki/Q818930","display_name":"Computability theory","level":2,"score":0.8419525623321533},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.6929474472999573},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.6888055801391602},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.5770508646965027},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5585087537765503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5522430539131165},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.5418968200683594},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.45682716369628906},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4376319646835327},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4299778938293457},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.4147490859031677},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32577669620513916},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31969916820526123},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2909930944442749},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1916634440422058},{"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/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2271945","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271945","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1816556148","https://openalex.org/W2059568104","https://openalex.org/W2062135743","https://openalex.org/W2063706894","https://openalex.org/W2066091881","https://openalex.org/W2072643132","https://openalex.org/W2086873580","https://openalex.org/W2140518055","https://openalex.org/W2168321497","https://openalex.org/W2530006810","https://openalex.org/W2554842236","https://openalex.org/W2905135108","https://openalex.org/W4236814057","https://openalex.org/W6665536099"],"related_works":["https://openalex.org/W2001962035","https://openalex.org/W2089947806","https://openalex.org/W2086873580","https://openalex.org/W95138543","https://openalex.org/W2070295070","https://openalex.org/W2186864846","https://openalex.org/W2185077833","https://openalex.org/W102922957","https://openalex.org/W2914940747","https://openalex.org/W100398054"],"abstract_inverted_index":{"Early":[0],"work":[1,80,167],"combining":[2],"recursion":[3,20,95],"theory":[4,21,96],"and":[5,83,137,159,170],"algebra":[6,98,109],"had":[7],"(at":[8],"least)":[9],"two":[10],"different":[11],"sets":[12],"of":[13,19,37,50,73,76,81,94,118,129,145,157,168],"motivations.":[14],"First":[15],"the":[16,32,44,48,61,79,92,111,116,140,155,166],"precise":[17],"setting":[18],"offered":[22],"a":[23,67,188,198,205,208],"chance":[24],"to":[25,31,97,106,204],"make":[26],"formal":[27],"classical":[28],"concerns":[29],"as":[30,121],"effective":[33],"or":[34],"algorithmic":[35],"nature":[36],"algebraic":[38],"constructions.":[39],"As":[40],"an":[41],"added":[42,141],"benefit":[43],"formalization":[45],"gives":[46],"one":[47,193],"opportunity":[49],"proving":[51],"that":[52,144,192],"certain":[53],"constructions":[54],"cannot":[55,194],"be":[56],"done":[57],"effectively":[58,196],"even":[59],"when":[60],"original":[62],"data":[63],"is":[64,78,99,132,143,165],"presented":[65],"in":[66,86,134,154,187],"recursive":[68,146],"way.":[69],"One":[70,104],"important":[71],"example":[72,128],"this":[74,130],"sort":[75,131],"approach":[77],"Frohlich":[82],"Shepardson":[84],"[1955]":[85],"field":[87],"theory.":[88,126],"Another":[89,127],"motivation":[90],"for":[91,179,207],"introduction":[93],"given":[100,199],"by":[101,110,115],"Rabin":[102],"[1960].":[103],"hopes":[105],"mathematically":[107],"enrich":[108],"additional":[112],"structure":[113,123,142],"provided":[114,133],"notion":[117],"computability":[119],"much":[120],"topological":[122],"enriches":[124],"group":[125],"Dekker":[135],"[1969]":[136],"[1971]":[138],"where":[139],"equivalence":[147],"types.":[148],"(This":[149],"particular":[150],"structural":[151],"view":[152],"culminates":[153],"monograph":[156],"Crossley":[158],"Nerode":[160,171],"[1974].)":[161],"More":[162],"recently":[163],"there":[164],"Metakides":[169],"[1975],":[172],"[1977]":[173],"which":[174],"combines":[175],"both":[176],"approaches.":[177],"Thus,":[178],"example,":[180],"working":[181],"with":[182],"vector":[183,210],"spaces":[184],"they":[185],"show":[186],"very":[189],"strong":[190],"way":[191],"always":[195],"extend":[197],"(even":[200],"recursive)":[201],"independent":[202],"set":[203],"basis":[206],"(recursive)":[209],"space.":[211]},"counts_by_year":[{"year":2021,"cited_by_count":15},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}