{"id":"https://openalex.org/W2766922222","doi":"https://doi.org/10.1007/s00153-018-0650-3","title":"Degrees of bi-embeddable categoricity of equivalence structures","display_name":"Degrees of bi-embeddable categoricity of equivalence structures","publication_year":2018,"publication_date":"2018-11-01","ids":{"openalex":"https://openalex.org/W2766922222","doi":"https://doi.org/10.1007/s00153-018-0650-3","mag":"2766922222"},"language":"en","primary_location":{"id":"doi:10.1007/s00153-018-0650-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-018-0650-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-018-0650-3.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00153-018-0650-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084964581","display_name":"Nikolay Bazhenov","orcid":"https://orcid.org/0000-0002-5834-2770"},"institutions":[{"id":"https://openalex.org/I188973947","display_name":"Novosibirsk State University","ror":"https://ror.org/04t2ss102","country_code":"RU","type":"education","lineage":["https://openalex.org/I188973947"]},{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Nikolay Bazhenov","raw_affiliation_strings":["Novosibirsk State University, 2 Pirogova St., Novosibirsk, Russia, 630090","Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., Novosibirsk, Russia, 630090"],"affiliations":[{"raw_affiliation_string":"Novosibirsk State University, 2 Pirogova St., Novosibirsk, Russia, 630090","institution_ids":["https://openalex.org/I188973947"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., Novosibirsk, Russia, 630090","institution_ids":["https://openalex.org/I4210096862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084954961","display_name":"Ekaterina Fokina","orcid":"https://orcid.org/0000-0002-4598-458X"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Ekaterina Fokina","raw_affiliation_strings":["Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstra\u00dfe 8\u201310, 1040, Wien, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstra\u00dfe 8\u201310, 1040, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010111113","display_name":"Dino Rossegger","orcid":"https://orcid.org/0000-0003-3494-9049"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Dino Rossegger","raw_affiliation_strings":["Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstra\u00dfe 8\u201310, 1040, Wien, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstra\u00dfe 8\u201310, 1040, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011087960","display_name":"Luca San Mauro","orcid":"https://orcid.org/0000-0002-3156-6870"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Luca San Mauro","raw_affiliation_strings":["Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstra\u00dfe 8\u201310, 1040, Wien, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstra\u00dfe 8\u201310, 1040, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5084964581"],"corresponding_institution_ids":["https://openalex.org/I188973947","https://openalex.org/I4210096862"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.2824,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.81302395,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"58","issue":"5-6","first_page":"543","last_page":"563"},"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/T11567","display_name":"semigroups and automata theory","score":0.9958000183105469,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/equivalence","display_name":"Equivalence (formal languages)","score":0.7838833332061768},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7719579935073853},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.6071435213088989},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4361257255077362},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3765002489089966},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37200692296028137}],"concepts":[{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.7838833332061768},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7719579935073853},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.6071435213088989},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4361257255077362},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3765002489089966},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37200692296028137}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00153-018-0650-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-018-0650-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-018-0650-3.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1710.10927","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.10927","pdf_url":"https://arxiv.org/pdf/1710.10927","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":"pmh:oai:ricerca.uniba.it:11586/454551","is_oa":false,"landing_page_url":"https://hdl.handle.net/11586/454551","pdf_url":null,"source":{"id":"https://openalex.org/S4377196296","display_name":"CINECA IRIS Institutional Research Information System (University of Bari Aldo Moro)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5561750","host_organization_name":"University of Bari Aldo Moro","host_organization_lineage":["https://openalex.org/I5561750"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:usiena-air.unisi.it:11365/1115996","is_oa":true,"landing_page_url":"http://hdl.handle.net/11365/1115996","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00153-018-0650-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-018-0650-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-018-0650-3.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3834316607","display_name":null,"funder_award_id":"16-31-60058 mol_a_dk","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G4723655159","display_name":null,"funder_award_id":"P 27527","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5997868131","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G6631171894","display_name":null,"funder_award_id":"P27527","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G8184292771","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2766922222.pdf","grobid_xml":"https://content.openalex.org/works/W2766922222.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W262335649","https://openalex.org/W1981473293","https://openalex.org/W1996647670","https://openalex.org/W2004277670","https://openalex.org/W2013474162","https://openalex.org/W2043078465","https://openalex.org/W2063706894","https://openalex.org/W2065144039","https://openalex.org/W2150583267","https://openalex.org/W2209102811","https://openalex.org/W2316087080","https://openalex.org/W2484528249","https://openalex.org/W2510730833","https://openalex.org/W2802461792","https://openalex.org/W2885232746","https://openalex.org/W2970889987"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W1976691234","https://openalex.org/W4287664878","https://openalex.org/W2499765358","https://openalex.org/W2349728712"],"abstract_inverted_index":{"We":[0,11,45,71,91],"study":[1,38],"the":[2,13,33,39,48,96],"algorithmic":[3],"complexity":[4,40,99],"of":[5,15,27,41,50,80,100],"embeddings":[6],"between":[7,43],"bi-embeddable":[8,17,23,28,54,61,81],"equivalence":[9,65,76,102],"structures.":[10,44],"define":[12],"notions":[14,31,35,49],"computable":[16,75,101],"categoricity,":[18,24],"(relative)":[19],"$$\\Delta":[20,51,58],"^0_\\alpha":[21,52,59],"$$":[22,53,60],"and":[25,56],"degrees":[26],"categoricity.":[29],"These":[30],"mirror":[32],"classical":[34],"used":[36],"to":[37,106],"isomorphisms":[42],"show":[46],"that":[47,74],"categoricity":[55,62,82],"relative":[57],"coincide":[63],"for":[64,67],"structures":[66,77],"$$\\alpha":[68],"=1,2,3$$":[69],".":[70,90],"also":[72],"prove":[73],"have":[78],"degree":[79],"$$\\mathbf":[83,88],"{0},\\mathbf":[84],"{0}'$$":[85],",":[86],"or":[87],"{0}''$$":[89],"furthermore":[92],"obtain":[93],"results":[94],"on":[95],"index":[97],"set":[98],"structure":[103],"with":[104],"respect":[105],"bi-embeddability.":[107]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}