{"id":"https://openalex.org/W2046880643","doi":"https://doi.org/10.2307/421207","title":"Degree Spectra of Relations on Computable Structures","display_name":"Degree Spectra of Relations on Computable Structures","publication_year":2000,"publication_date":"2000-06-01","ids":{"openalex":"https://openalex.org/W2046880643","doi":"https://doi.org/10.2307/421207","mag":"2046880643"},"language":"en","primary_location":{"id":"doi:10.2307/421207","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421207","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin 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/A5015485533","display_name":"Denis R. Hirschfeldt","orcid":null},"institutions":[{"id":"https://openalex.org/I41156924","display_name":"Victoria University of Wellington","ror":"https://ror.org/0040r6f76","country_code":"NZ","type":"education","lineage":["https://openalex.org/I41156924"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Denis R. Hirschfeldt","raw_affiliation_strings":["School of Mathematical and Computing Sciences, Victoria University of Wellington, New zealand E-mail:"],"affiliations":[{"raw_affiliation_string":"School of Mathematical and Computing Sciences, Victoria University of Wellington, New zealand E-mail:","institution_ids":["https://openalex.org/I41156924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015485533"],"corresponding_institution_ids":["https://openalex.org/I41156924"],"apc_list":null,"apc_paid":null,"fwci":0.4684,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.67023634,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"6","issue":"2","first_page":"197","last_page":"212"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9196000099182129,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.7094069719314575},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6725612878799438},{"id":"https://openalex.org/keywords/successor-cardinal","display_name":"Successor cardinal","score":0.6600110530853271},{"id":"https://openalex.org/keywords/computable-number","display_name":"Computable number","score":0.5892698168754578},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.5253557562828064},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5212771892547607},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.4298766851425171},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4080687463283539},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3843056559562683},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33296626806259155}],"concepts":[{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.7094069719314575},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6725612878799438},{"id":"https://openalex.org/C75306776","wikidata":"https://www.wikidata.org/wiki/Q7632662","display_name":"Successor cardinal","level":2,"score":0.6600110530853271},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.5892698168754578},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.5253557562828064},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5212771892547607},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.4298766851425171},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4080687463283539},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3843056559562683},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33296626806259155},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","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/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.2307/421207","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421207","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1182353687","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1182353687","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.114.8618","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.114.8618","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uchicago.edu/~drh/Papers/delta2.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.117.3721","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.3721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cornell.edu/~shore/theses/denis.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.133.1554","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.133.1554","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uchicago.edu/~drh/Papers/ths.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1026721552","https://openalex.org/W1556584770","https://openalex.org/W1593660953","https://openalex.org/W1975720205","https://openalex.org/W1979974835","https://openalex.org/W1980268869","https://openalex.org/W1989997916","https://openalex.org/W1991087857","https://openalex.org/W1992539853","https://openalex.org/W1996816738","https://openalex.org/W2007016528","https://openalex.org/W2010770007","https://openalex.org/W2025254909","https://openalex.org/W2032686575","https://openalex.org/W2033918725","https://openalex.org/W2043188238","https://openalex.org/W2044599705","https://openalex.org/W2044797614","https://openalex.org/W2056414301","https://openalex.org/W2068530698","https://openalex.org/W2087519684","https://openalex.org/W2131332739","https://openalex.org/W2317860071","https://openalex.org/W2327605742","https://openalex.org/W3024069397","https://openalex.org/W4231791887","https://openalex.org/W4232277851","https://openalex.org/W6656403195"],"related_works":["https://openalex.org/W2150482238","https://openalex.org/W197714092","https://openalex.org/W1577501449","https://openalex.org/W153068418","https://openalex.org/W2527631632","https://openalex.org/W1994403863","https://openalex.org/W2108904240","https://openalex.org/W1987175852","https://openalex.org/W1498085647","https://openalex.org/W2080359559"],"abstract_inverted_index":{"There":[0],"has":[1,24,203,220,233],"been":[2,25,95],"increasing":[3],"interest":[4],"over":[5],"the":[6,11,14,26,39,49,54,57,70,81,126,145,150,172,200,241],"last":[7],"few":[8],"decades":[9],"in":[10,170,198],"study":[12],"of":[13,17,28,32,83,89,91,128,130,148,167,195,218,231,237,243],"effective":[15,22],"content":[16,23],"Mathematics.":[18],"One":[19],"field":[20],"whose":[21,110],"subject":[27],"a":[29,163,191,221,234],"large":[30],"body":[31],"work,":[33],"dating":[34],"back":[35],"at":[36],"least":[37],"to":[38,80,161,210,250],"early":[40],"1960s,":[41],"is":[42,48,99,154,158,175,207,252],"model":[43,119,132,245],"theory.":[44],"(A":[45],"valuable":[46],"reference":[47],"handbook":[50],"[7].":[51],"In":[52,118,178],"particular,":[53],"introduction":[55],"and":[56,61,63,74,113],"articles":[58,71],"by":[59,64,72,75],"Ershov":[60],"Goncharov":[62,76],"Harizanov":[65],"give":[66],"useful":[67],"overviews,":[68],"while":[69],"Ash":[73],"cover":[77],"material":[78],"related":[79],"topic":[82],"this":[84],"communication.)":[85],"Several":[86],"different":[87],"notions":[88],"effectiveness":[90],"model-theoretic":[92],"structures":[93,106,137,248],"have":[94],"investigated.":[96],"This":[97],"communication":[98],"concerned":[100],"with":[101,107],"computable":[102,108,131,164,192,214,222,235,244],"structures,":[103],"that":[104],"is,":[105],"domains":[109],"constants,":[111],"functions,":[112],"relations":[114],"are":[115],"uniformly":[116],"computable.":[117,177],"theory,":[120,133,246],"we":[121,188],"identify":[122],"isomorphic":[123,136,213,226],"structures.":[124],"From":[125],"point":[127],"view":[129],"however,":[134],"two":[135,212,225],"might":[138],"be":[139],"very":[140],"different.":[141],"For":[142],"example,":[143],"under":[144],"standard":[146],"ordering":[147,166,194],"\u03c9":[149,169,197],"success":[151],"or":[152,224],"relation":[153,174,202],"computable,":[155],"but":[156],"it":[157],"not":[159,176,253],"hard":[160],"construct":[162,190],"linear":[165,193],"type":[168,196],"which":[171,199,219,232],"successor":[173,201],"fact,":[179],"for":[180,240],"every":[181],"computably":[182],"enumerable":[183],"(c.":[184],"e.)":[185],"degree":[186,204],"a,":[187],"can":[189],"a.":[205],"It":[206],"also":[208],"possible":[209],"build":[211],"groups,":[215],"only":[216,229],"one":[217,230],"center,":[223],"Boolean":[227],"algebras,":[228],"set":[236],"atoms.":[238],"Thus,":[239],"purposes":[242],"studying":[247],"up":[249],"isomorphism":[251],"enough.":[254]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
