{"id":"https://openalex.org/W2069764971","doi":"https://doi.org/10.2307/2271892","title":"A survey of partial degrees","display_name":"A survey of partial degrees","publication_year":1975,"publication_date":"1975-06-01","ids":{"openalex":"https://openalex.org/W2069764971","doi":"https://doi.org/10.2307/2271892","mag":"2069764971"},"language":"en","primary_location":{"id":"doi:10.2307/2271892","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271892","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/A5073277979","display_name":"Leonard P. Sasso","orcid":null},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]},{"id":"https://openalex.org/I2803209242","display_name":"University of California System","ror":"https://ror.org/00pjdza24","country_code":"US","type":"education","lineage":["https://openalex.org/I2803209242"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Leonard P. Sasso","raw_affiliation_strings":["University of California, Irvine, California 92664","University of California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Irvine, California 92664","institution_ids":["https://openalex.org/I204250578"]},{"raw_affiliation_string":"University of California","institution_ids":["https://openalex.org/I2803209242"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073277979"],"corresponding_institution_ids":["https://openalex.org/I204250578","https://openalex.org/I2803209242"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":2.6619,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.91915423,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"40","issue":"2","first_page":"130","last_page":"140"},"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":0.9941999912261963,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9897000193595886,"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/partial-function","display_name":"Partial function","score":0.7350148558616638},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6649908423423767},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.48773393034935},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.46187281608581543},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4596019387245178},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.43642663955688477},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.43151235580444336},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4180455207824707},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3635595142841339},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3283538222312927},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17513597011566162},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07178851962089539}],"concepts":[{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.7350148558616638},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6649908423423767},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.48773393034935},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.46187281608581543},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4596019387245178},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.43642663955688477},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.43151235580444336},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4180455207824707},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3635595142841339},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3283538222312927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17513597011566162},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07178851962089539},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2271892","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271892","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/1183739373","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183739373","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1483568252","https://openalex.org/W1547216710","https://openalex.org/W1967629533","https://openalex.org/W2024373817","https://openalex.org/W2042499838","https://openalex.org/W2055051664","https://openalex.org/W2055606729","https://openalex.org/W2060075008","https://openalex.org/W2069624526","https://openalex.org/W2087882664","https://openalex.org/W2530006810","https://openalex.org/W2565699923","https://openalex.org/W2797656628","https://openalex.org/W2905135108","https://openalex.org/W4248519925","https://openalex.org/W6829772892"],"related_works":["https://openalex.org/W2155753715","https://openalex.org/W1912967923","https://openalex.org/W2499765358","https://openalex.org/W2349728712","https://openalex.org/W2162114838","https://openalex.org/W2184512187","https://openalex.org/W2279903697","https://openalex.org/W2116465509","https://openalex.org/W2391796915","https://openalex.org/W2370856440"],"abstract_inverted_index":{"Partial":[0],"degrees":[1,116],"are":[2,33,117,147],"equivalence":[3],"classes":[4],"of":[5,14,23,30,42,52,59,71,76,78,80,83,98,106,131,142,160,195,207,217,231],"partial":[6,18,38,57,60,88,99,132,140,143,238],"natural":[7],"number":[8],"functions":[9,61,100,133,197,219],"under":[10,220],"some":[11],"suitable":[12],"extension":[13,70],"relative":[15,24,81,87,107,139,193,227],"recursiveness":[16,58,82,89,141,194],"to":[17,37,46,92,137,149,166],"functions.":[19,39,85,144],"The":[20,40,114],"usual":[21],"definitions":[22,233],"recursiveness,":[25],"equivalent":[26,91,148],"in":[27,65,154,190],"the":[28,48,53,72,93,96,150,169,215],"context":[29],"total":[31,84,196],"functions,":[32,239],"distinct":[34],"when":[35],"extended":[36],"purpose":[41],"this":[43],"paper":[44],"is":[45,90,164,177,183,245],"compare":[47],"upper":[49],"semilattice":[50],"structures":[51],"resulting":[54,115,170],"degrees.":[55,121],"Relative":[56],"was":[62],"first":[63],"introduced":[64,153],"Kleene":[66],"[2]":[67,123],"as":[68,214],"an":[69],"definition":[73],"by":[74,102,205],"means":[75,206],"systems":[77],"equations":[79],"Kleene's":[86],"relation":[94,105,236],"between":[95,112,237],"graphs":[97],"induced":[101],"Rogers'":[103],"[10]":[104,156],"enumerability":[108],"(called":[109],"enumeration":[110,120,187],"reducibility)":[111],"sets.":[113],"hence":[118],"called":[119,173,241],"In":[122],"Davis":[124,191],"introduces":[125],"completely":[126],"computable":[127],"or":[128,212],"compact":[129],"functionals":[130,146],"and":[134,162,224],"uses":[135],"these":[136,232],"define":[138],"Davis'":[145],"recursive":[151],"operators":[152],"Rogers":[155],"where":[157],"a":[158,235],"theorem":[159],"Myhill":[161],"Shepherdson":[163],"used":[165],"show":[167],"that":[168],"reducibility,":[171,176,243],"here":[172,240],"weak":[174],"Turing":[175,208,242],"stronger":[178,246],"than":[179],"(i.e.,":[180,226],"implies,":[181],"but":[182],"not":[184],"implied":[185],"by)":[186],"reducibility.":[188],"As":[189],"[2],":[192],"with":[198,210],"range":[199],"\u2286{0,":[200],"1}":[201],"may":[202],"be":[203],"defined":[204],"machines":[209],"oracles":[211],"equivalently":[213],"closure":[216],"initial":[218],"composition,":[221],"primitive":[222],"re-cursion,":[223],"minimalization":[225],"\u03bc-recursiveness).":[228],"Extending":[229],"either":[230],"yields":[234],"which":[244],"still.":[247]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}