{"id":"https://openalex.org/W2148849878","doi":"https://doi.org/10.1002/malq.19960420121","title":"Effectively and Noneffectively Nowhere Simple Sets","display_name":"Effectively and Noneffectively Nowhere Simple Sets","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2148849878","doi":"https://doi.org/10.1002/malq.19960420121","mag":"2148849878"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19960420121","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19960420121","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5071875842","display_name":"Valentina Harizanov","orcid":"https://orcid.org/0000-0002-6626-5074"},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Valentina S. Harizanov","raw_affiliation_strings":["Department of Mathematics, The George Washington University, 2201 G Street, N.W., Funger Hall, Washington, D. C. 20052, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The George Washington University, 2201 G Street, N.W., Funger Hall, Washington, D. C. 20052, U.S.A","institution_ids":["https://openalex.org/I193531525"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071875842"],"corresponding_institution_ids":["https://openalex.org/I193531525"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.5107,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69014213,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":"1","first_page":"241","last_page":"248"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9898999929428101,"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":0.9708999991416931,"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/simple","display_name":"Simple (philosophy)","score":0.8530793190002441},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.8225657939910889},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7958997488021851},{"id":"https://openalex.org/keywords/nowhere-dense-set","display_name":"Nowhere dense set","score":0.7914279699325562},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.7250452041625977},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.6315594911575317},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6270082592964172},{"id":"https://openalex.org/keywords/maximal-set","display_name":"Maximal set","score":0.5030497908592224},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46697402000427246},{"id":"https://openalex.org/keywords/disjoint-union","display_name":"Disjoint union (topology)","score":0.46515899896621704},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4273451566696167},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3833887577056885},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10760146379470825}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.8530793190002441},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.8225657939910889},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7958997488021851},{"id":"https://openalex.org/C17327563","wikidata":"https://www.wikidata.org/wiki/Q1991405","display_name":"Nowhere dense set","level":3,"score":0.7914279699325562},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.7250452041625977},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.6315594911575317},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6270082592964172},{"id":"https://openalex.org/C188521023","wikidata":"https://www.wikidata.org/wiki/Q6795644","display_name":"Maximal set","level":3,"score":0.5030497908592224},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46697402000427246},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.46515899896621704},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4273451566696167},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3833887577056885},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10760146379470825},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/malq.19960420121","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19960420121","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.404.5882","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.404.5882","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://home.gwu.edu/~harizanv/nss.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","score":0.7699999809265137,"id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W2015707592","https://openalex.org/W2029116149","https://openalex.org/W2056414301","https://openalex.org/W2070295070","https://openalex.org/W2077886582","https://openalex.org/W2530006810","https://openalex.org/W2905135108","https://openalex.org/W4232277851","https://openalex.org/W4234742723"],"related_works":["https://openalex.org/W2037833610","https://openalex.org/W2089792255","https://openalex.org/W2135152748","https://openalex.org/W2069987267","https://openalex.org/W1973052363","https://openalex.org/W1972481159","https://openalex.org/W2112189052","https://openalex.org/W2000487993","https://openalex.org/W1980641386","https://openalex.org/W4249600134"],"abstract_inverted_index":{"Abstract":[0],"R.":[1,144],"Shore":[2,145],"proved":[3,146],"that":[4,94,147,169,178,191],"every":[5,95,122,135,149,192],"recursively":[6],"enumerable":[7],"(r.":[8],"e.)":[9],"set":[10,98,153,175,203],"can":[11,67,82],"be":[12,68,83],"split":[13,69,84],"into":[14,70,85,126,139],"two":[15,71,86,105,111],"(disjoint)":[16],"nowhere":[17,74,107,113,127,141,151,173,201],"simple":[18,43,75,90,108,114,128,142,152,174,202],"sets.":[19,41,91,115,143],"Splitting":[20],"theorems":[21],"play":[22],"an":[23],"important":[24],"role":[25],"in":[26],"recursion":[27],"theory":[28],"since":[29],"they":[30],"provide":[31],"information":[32],"about":[33],"the":[34,101,156,206],"lattice":[35,157,207],"\u03f5":[36],"of":[37,58,104],"all":[38],"r.":[39,63,78,87,96,118,131,194],"e.":[40,64,79,88,97,119,132,195],"Nowhere":[42],"sets":[44,65,80,109,120,133],"were":[45],"further":[46],"studied":[47],"by":[48],"D.":[49],"Miller":[50],"and":[51,54,77,130,168],"J.":[52],"Remmel,":[53],"we":[55],"generalize":[56],"some":[57],"their":[59],"results.":[60],"We":[61,92,116,189],"characterize":[62,117],"which":[66,81],"(non)":[72],"effectively":[73,106,140,150,164,185,212],"sets,":[76,129],"non\u2010nowhere":[89],"show":[93],"is":[99,125,138,163,171,183],"either":[100],"disjoint":[102],"union":[103],"or":[110],"noneffectively":[112,200],"whose":[121,134],"nontrivial":[123,136],"splitting":[124,137],"for":[148],"A":[154,161,176,181,204,210],",":[155],"L":[158,179,208],"*":[159],"(":[160],")":[162,182,211],"isomorphic":[165,186,213],"to":[166,187,214],"\u03f5*,":[167],"there":[170],"a":[172,199],"such":[177],"*(":[180,209],"not":[184],"\u03f5*.":[188,215],"prove":[190],"nonzero":[193],"Turing":[196],"degree":[197],"contains":[198],"with":[205],"Mathematics":[216],"Subject":[217],"Classification:":[218],"03D25,":[219],"03D10.":[220]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}