{"id":"https://openalex.org/W2294316973","doi":"https://doi.org/10.1002/malq.201500057","title":"Weakly precomplete computably enumerable equivalence relations","display_name":"Weakly precomplete computably enumerable equivalence relations","publication_year":2016,"publication_date":"2016-02-01","ids":{"openalex":"https://openalex.org/W2294316973","doi":"https://doi.org/10.1002/malq.201500057","mag":"2294316973"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201500057","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201500057","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11365/990179","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082479324","display_name":"S. A. Badaev","orcid":"https://orcid.org/0000-0003-0444-2394"},"institutions":[{"id":"https://openalex.org/I185571130","display_name":"Al-Farabi Kazakh National University","ror":"https://ror.org/03q0vrn42","country_code":"KZ","type":"education","lineage":["https://openalex.org/I185571130"]}],"countries":["KZ"],"is_corresponding":true,"raw_author_name":"Serikzhan Badaev","raw_affiliation_strings":["Department of Mechanics and Mathematics Al\u2010Farabi Kazakh National University Almaty 050038 Kazakhstan","Department of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty, 050038 Kazakhstan"],"affiliations":[{"raw_affiliation_string":"Department of Mechanics and Mathematics Al\u2010Farabi Kazakh National University Almaty 050038 Kazakhstan","institution_ids":["https://openalex.org/I185571130"]},{"raw_affiliation_string":"Department of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty, 050038 Kazakhstan","institution_ids":["https://openalex.org/I185571130"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068865870","display_name":"Andrea Sorbi","orcid":"https://orcid.org/0000-0001-9288-3290"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Andrea Sorbi","raw_affiliation_strings":["Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche Universit\u00e0 Degli Studi di Siena 53100 Siena Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche Universit\u00e0 Degli Studi di Siena 53100 Siena Italy","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068865870","https://openalex.org/A5082479324"],"corresponding_institution_ids":["https://openalex.org/I102064193","https://openalex.org/I185571130"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":2.0908,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.87616261,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"62","issue":"1-2","first_page":"111","last_page":"127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9986000061035156,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9937999844551086,"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/mathematics","display_name":"Mathematics","score":0.9269819855690002},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.8324220180511475},{"id":"https://openalex.org/keywords/equivalence-class","display_name":"Equivalence class (music)","score":0.5536110997200012},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5365068912506104},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.5216132402420044},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49517694115638733},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44089895486831665},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4353015422821045},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.4282096028327942},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41590166091918945},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.41342997550964355}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9269819855690002},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.8324220180511475},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.5536110997200012},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5365068912506104},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.5216132402420044},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49517694115638733},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44089895486831665},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4353015422821045},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.4282096028327942},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41590166091918945},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.41342997550964355},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","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},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/malq.201500057","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201500057","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["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:usiena-air.unisi.it:11365/990179","is_oa":true,"landing_page_url":"http://hdl.handle.net/11365/990179","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:usiena-air.unisi.it:11365/990179","is_oa":true,"landing_page_url":"http://hdl.handle.net/11365/990179","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.47999998927116394,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W818805751","https://openalex.org/W1636748716","https://openalex.org/W1909320839","https://openalex.org/W1980790864","https://openalex.org/W1987946099","https://openalex.org/W1992313178","https://openalex.org/W2037469541","https://openalex.org/W2053099695","https://openalex.org/W2058701006","https://openalex.org/W2068423429","https://openalex.org/W2084753590","https://openalex.org/W2091083565","https://openalex.org/W2905135108","https://openalex.org/W3103324540","https://openalex.org/W4230007549"],"related_works":["https://openalex.org/W2895616265","https://openalex.org/W2499765358","https://openalex.org/W2026098892","https://openalex.org/W2382232876","https://openalex.org/W2593727555","https://openalex.org/W124507830","https://openalex.org/W2148887744","https://openalex.org/W4298221493","https://openalex.org/W2362545535","https://openalex.org/W2349728712"],"abstract_inverted_index":{"Using":[0],"computable":[1],"reducibility":[2],"\u2a7d":[3],"on":[4,20],"equivalence":[5,18,141],"relations,":[6],"we":[7,25,118,146,179],"investigate":[8],"weakly":[9,53,70,90,122,135,166],"precomplete":[10,35,54,71,79,91,108,123,136,154,167,189],"ceers":[11,55,92,109,124,137,155,168,190,195],"(a":[12],"\u201cceer\u201d":[13],"is":[14,143,156,169],"a":[15,78,104,174],"computably":[16,129],"enumerable":[17],"relation":[19],"the":[21,30,74,149,153,161,165,183,187,193],"natural":[22],"numbers),":[23],"and":[24,61,191],"compare":[26],"their":[27],"class":[28,33,142],"with":[29],"more":[31],"restricted":[32],"of":[34,46,68,77,152,164,176,186,192],"ceers.":[36,72],"We":[37],"show":[38,119,147,181],"that":[39,57,120,148,182],"there":[40,62,88,133],"are":[41,58,63,134,196],"infinitely":[42,64],"many":[43,65],"isomorphism":[44,66],"types":[45,67],"universal":[47],"(in":[48],"fact":[49],"uniformly":[50,188],"finitely":[51],"precomplete)":[52],",":[56],"not":[59,97],"precomplete;":[60],"non\u2010universal":[69],"Whereas":[73],"Visser":[75,94],"space":[76],"ceer":[80],"always":[81,111,125],"contains":[82],"an":[83],"infinite":[84,99],"effectively":[85,100,115],"discrete":[86,101],"subset,":[87],"exist":[89],"whose":[93],"spaces":[95],"do":[96],"contain":[98],"subsets.":[102],"As":[103,173],"consequence,":[105],"contrary":[106],"to":[107],"which":[110,139],"yield":[112,126],"partitions":[113,127],"into":[114,128],"inseparable":[116,130],"sets,":[117,131],"although":[121],"nevertheless":[132],"for":[138],"no":[140],"creative.":[144],"Finally,":[145],"index":[150,162,184],"set":[151,163],"\u03a3":[157,197],"3":[158,171,198],"\u2010complete,":[159],"whereas":[160],"\u03a0":[170],"\u2010complete.":[172,199],"consequence":[175],"these":[177],"results,":[178],"also":[180],"sets":[185],"e\u2010complete":[194]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
