{"id":"https://openalex.org/W2081822213","doi":"https://doi.org/10.2307/2275258","title":"The degrees of conditional problems","display_name":"The degrees of conditional problems","publication_year":1994,"publication_date":"1994-03-01","ids":{"openalex":"https://openalex.org/W2081822213","doi":"https://doi.org/10.2307/2275258","mag":"2081822213"},"language":"en","primary_location":{"id":"doi:10.2307/2275258","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275258","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":null,"display_name":"Su Gao","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Su Gao","raw_affiliation_strings":["Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90024, E-mail:","University of California at Los Angeles**"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90024, E-mail:","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"University of California at Los Angeles**","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.4347,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64348227,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"1","first_page":"166","last_page":"181"},"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":0.9968000054359436,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9804999828338623,"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/turing","display_name":"Turing","score":0.760619044303894},{"id":"https://openalex.org/keywords/distributive-lattice","display_name":"Distributive lattice","score":0.5836546421051025},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5640757083892822},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5513789057731628},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5331313610076904},{"id":"https://openalex.org/keywords/conditional-expectation","display_name":"Conditional expectation","score":0.41278186440467834},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38299161195755005},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3525201678276062},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.34350520372390747},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32503727078437805},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.301887571811676},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11457952857017517},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10833302140235901},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09130564332008362}],"concepts":[{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.760619044303894},{"id":"https://openalex.org/C192606457","wikidata":"https://www.wikidata.org/wiki/Q2363730","display_name":"Distributive lattice","level":3,"score":0.5836546421051025},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5640757083892822},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5513789057731628},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5331313610076904},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.41278186440467834},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38299161195755005},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3525201678276062},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.34350520372390747},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32503727078437805},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.301887571811676},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11457952857017517},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10833302140235901},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09130564332008362},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2275258","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275258","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/1183744442","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183744442","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":3,"referenced_works":["https://openalex.org/W2056414301","https://openalex.org/W2500837594","https://openalex.org/W2530006810"],"related_works":["https://openalex.org/W4232534867","https://openalex.org/W2037861231","https://openalex.org/W2122961867","https://openalex.org/W2963428356","https://openalex.org/W2307047024","https://openalex.org/W1975062576","https://openalex.org/W871156903","https://openalex.org/W1804250731","https://openalex.org/W2126448176","https://openalex.org/W2349761759"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4],"define":[5],"and":[6,10,31,64,73],"study":[7],"conditional":[8,21,50],"problems":[9,63],"their":[11,65],"degrees.":[12,43,74],"The":[13],"main":[14],"result":[15],"is":[16,23,33,53],"that":[17,46],"the":[18,27,47],"class":[19,48],"of":[20,49,61],"degrees":[22,30,52],"a":[24,54],"lattice":[25],"extending":[26],"ordinary":[28,41],"Turing":[29,42],"it":[32],"dense.":[34],"These":[35],"properties":[36,60],"are":[37,68],"not":[38],"shared":[39],"by":[40],"We":[44,57],"show":[45],"many-one":[51],"distributive":[55],"lattice.":[56],"also":[58],"consider":[59],"semidecidable":[62],"degrees,":[66],"which":[67],"analogous":[69],"to":[70],"r.e.":[71],"sets":[72]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
