{"id":"https://openalex.org/W2291706836","doi":"https://doi.org/10.3233/com-160053","title":"Computably enumerable sets that are automorphic to low sets","display_name":"Computably enumerable sets that are automorphic to low sets","publication_year":2016,"publication_date":"2016-12-22","ids":{"openalex":"https://openalex.org/W2291706836","doi":"https://doi.org/10.3233/com-160053","mag":"2291706836"},"language":"en","primary_location":{"id":"doi:10.3233/com-160053","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-160053","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1510.04199","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062882161","display_name":"Peter Cholak","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Cholak","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, South Bend, IN, USA. cholak@nd.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, South Bend, IN, USA. cholak@nd.edu","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010019649","display_name":"Rachel Epstein","orcid":null},"institutions":[{"id":"https://openalex.org/I118020396","display_name":"Swarthmore College","ror":"https://ror.org/012dg8a96","country_code":"US","type":"education","lineage":["https://openalex.org/I118020396"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rachel Epstein","raw_affiliation_strings":["Department of Mathematics and Statistics, Swarthmore College, Swarthmore, PA, USA. rachel.epstein@swarthmore.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Swarthmore College, Swarthmore, PA, USA. rachel.epstein@swarthmore.edu","institution_ids":["https://openalex.org/I118020396"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02302767,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":"1","first_page":"23","last_page":"45"},"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":0.9861000180244446,"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":0.9771000146865845,"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/complement","display_name":"Complement (music)","score":0.9152732491493225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7297152280807495},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6253270506858826},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.491458535194397},{"id":"https://openalex.org/keywords/automorphic-form","display_name":"Automorphic form","score":0.482920378446579},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4340234100818634},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38846465945243835},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3223407566547394},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19450733065605164}],"concepts":[{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.9152732491493225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7297152280807495},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6253270506858826},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.491458535194397},{"id":"https://openalex.org/C132817261","wikidata":"https://www.wikidata.org/wiki/Q1134435","display_name":"Automorphic form","level":2,"score":0.482920378446579},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4340234100818634},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38846465945243835},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3223407566547394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19450733065605164},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3233/com-160053","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-160053","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1510.04199","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.04199","pdf_url":"https://arxiv.org/pdf/1510.04199","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"mag:2291706836","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1510.04199","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1510.04199","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1510.04199","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1510.04199","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.04199","pdf_url":"https://arxiv.org/pdf/1510.04199","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.6499999761581421,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1506639696","https://openalex.org/W1510551874","https://openalex.org/W1967059630","https://openalex.org/W1986918418","https://openalex.org/W2000779724","https://openalex.org/W2005402036","https://openalex.org/W2018594881","https://openalex.org/W2024348511","https://openalex.org/W2029116149","https://openalex.org/W2056414301","https://openalex.org/W2150311525","https://openalex.org/W2315181607","https://openalex.org/W2962874125","https://openalex.org/W4232277851"],"related_works":["https://openalex.org/W2963233618","https://openalex.org/W2046805782","https://openalex.org/W1514076924","https://openalex.org/W2015707592","https://openalex.org/W2047937662","https://openalex.org/W3093901634","https://openalex.org/W2767324680","https://openalex.org/W1971553070","https://openalex.org/W3151833102","https://openalex.org/W3043598095","https://openalex.org/W2003774222","https://openalex.org/W2762168036","https://openalex.org/W3098284102","https://openalex.org/W2912747938","https://openalex.org/W3161432936","https://openalex.org/W2049639420","https://openalex.org/W3106086156","https://openalex.org/W2036312696","https://openalex.org/W2015329281","https://openalex.org/W2963875122"],"abstract_inverted_index":{"We":[0],"work":[1,35],"with":[2],"the":[3],"structure":[4],"consisting":[5],"of":[6,36],"all":[7],"computably":[8],"enumerable":[9],"(c.e.)":[10],"sets":[11,25],"ordered":[12],"by":[13],"set":[14],"inclusion.":[15],"The":[16],"question":[17],"we":[18,39],"will":[19],"partially":[20],"address":[21],"is":[22],"which":[23],"c.e.":[24],"are":[26],"autormorphic":[27],"to":[28],"low":[29],"(or":[30],"low2":[31],")":[32],"sets.":[33],"Using":[34],"R.":[37],"Miller,":[38],"can":[40],"see":[41],"that":[42],"every":[43]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
