{"id":"https://openalex.org/W1984336238","doi":"https://doi.org/10.2178/jsl/1264433915","title":"Schnorr triviality and genericity","display_name":"Schnorr triviality and genericity","publication_year":2010,"publication_date":"2010-01-25","ids":{"openalex":"https://openalex.org/W1984336238","doi":"https://doi.org/10.2178/jsl/1264433915","mag":"1984336238"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1264433915","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1264433915","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":"The 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/A5049135726","display_name":"Johanna N. Y. Franklin","orcid":"https://orcid.org/0000-0002-7216-1562"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Johanna N.Y. Franklin","raw_affiliation_strings":["Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada, E-mail:","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049135726"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":1.0148,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.75722631,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"75","issue":"1","first_page":"191","last_page":"207"},"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":0.9976000189781189,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9950000047683716,"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/triviality","display_name":"Triviality","score":0.7153915166854858},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6064577102661133},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.5783174633979797},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5042790174484253},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43658193945884705},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38249436020851135},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27133145928382874},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09243941307067871}],"concepts":[{"id":"https://openalex.org/C2778795013","wikidata":"https://www.wikidata.org/wiki/Q945127","display_name":"Triviality","level":2,"score":0.7153915166854858},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6064577102661133},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.5783174633979797},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5042790174484253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43658193945884705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38249436020851135},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27133145928382874},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09243941307067871},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1264433915","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1264433915","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":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1264433915","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1264433915","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":13,"referenced_works":["https://openalex.org/W623765668","https://openalex.org/W1997555168","https://openalex.org/W2014032276","https://openalex.org/W2020311636","https://openalex.org/W2056414301","https://openalex.org/W2087642972","https://openalex.org/W2101746971","https://openalex.org/W2117944581","https://openalex.org/W2160493389","https://openalex.org/W2499081645","https://openalex.org/W4210959615","https://openalex.org/W4232277851","https://openalex.org/W4234205087"],"related_works":["https://openalex.org/W2070814711","https://openalex.org/W2376029318","https://openalex.org/W2011957396","https://openalex.org/W2388301251","https://openalex.org/W2013770701","https://openalex.org/W2951326186","https://openalex.org/W1965609966","https://openalex.org/W1791476549","https://openalex.org/W3013941779","https://openalex.org/W2964342945"],"abstract_inverted_index":{"Abstract":[0],"We":[1,10,65],"study":[2],"the":[3,78],"connection":[4],"between":[5],"Schnorr":[6,21,31,43,63,83],"triviality":[7],"and":[8,23,75],"genericity.":[9],"show":[11,76],"that":[12,37,57,77],"while":[13],"no":[14,24],"2-generic":[15],"is":[16,26,34,38],"Turing":[17,39,85],"equivalent":[18,40],"to":[19,29,41,70],"a":[20,30,35,42,53,72],"trivial":[22,84],"1-generic":[25,36,48],"tt":[27],"-equivalent":[28],"trivial,":[32],"there":[33],"trivial.":[44,64],"However,":[45],"every":[46],"such":[47],"must":[49],"be":[50],"high.":[51],"As":[52],"corollary,":[54],"we":[55],"prove":[56],"not":[58],"all":[59],"K":[60],"-trivials":[61],"are":[62,87,92],"also":[66],"use":[67],"these":[68],"techniques":[69],"extend":[71],"previous":[73],"result":[74],"bases":[79],"of":[80,82],"cones":[81],"degrees":[86],"precisely":[88],"those":[89],"whose":[90],"jumps":[91],"at":[93],"least":[94],"0\u2033.":[95]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
