{"id":"https://openalex.org/W1992333765","doi":"https://doi.org/10.1002/malq.200710035","title":"The Relation Reflection Scheme","display_name":"The Relation Reflection Scheme","publication_year":2008,"publication_date":"2008-01-30","ids":{"openalex":"https://openalex.org/W1992333765","doi":"https://doi.org/10.1002/malq.200710035","mag":"1992333765"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200710035","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200710035","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051943015","display_name":"Peter Aczel","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Peter Aczel","raw_affiliation_strings":["Department of Computer Science, University of Manchester, Manchester, M13 9PL, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Manchester, Manchester, M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051943015"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.4233,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.56952853,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"54","issue":"1","first_page":"5","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9830999970436096,"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"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9771999716758728,"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/constructive-set-theory","display_name":"Constructive set theory","score":0.9420744180679321},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.7864675521850586},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7785273790359497},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.7349960803985596},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6980730295181274},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.6764216423034668},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6363016366958618},{"id":"https://openalex.org/keywords/urelement","display_name":"Urelement","score":0.6226195693016052},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.5741615891456604},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.5727855563163757},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.5063658952713013},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49418333172798157},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.435005247592926},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.361916720867157},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14806875586509705},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0936005711555481},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0662727952003479}],"concepts":[{"id":"https://openalex.org/C556429856","wikidata":"https://www.wikidata.org/wiki/Q5164501","display_name":"Constructive set theory","level":5,"score":0.9420744180679321},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.7864675521850586},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7785273790359497},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.7349960803985596},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6980730295181274},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.6764216423034668},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6363016366958618},{"id":"https://openalex.org/C78550038","wikidata":"https://www.wikidata.org/wiki/Q1896657","display_name":"Urelement","level":5,"score":0.6226195693016052},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.5741615891456604},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.5727855563163757},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.5063658952713013},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49418333172798157},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.435005247592926},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.361916720867157},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14806875586509705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0936005711555481},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0662727952003479},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1002/malq.200710035","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200710035","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:pure.atira.dk:openaire_cris_publications/6e90eddd-f94a-49cb-990b-023c4558c6e7","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/6e90eddd-f94a-49cb-990b-023c4558c6e7","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Aczel, P 2008, 'The relation reflection scheme', Mathematical Logic Quarterly, vol. 54, no. 1, pp. 5-11. https://doi.org/10.1002/malq.200710035","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.115.4689","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.4689","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.man.ac.uk/~petera/rrs.pdf","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/2415a528-e225-4e47-886a-866664f9ab31","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/2415a528-e225-4e47-886a-866664f9ab31","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aczel, P 2008, The relation reflection scheme. in Mathematical Logic Quarterly|Math. Logic Q.. vol. 54, John Wiley & Sons Ltd, pp. 5-11, Workshop on Trends in Constructive Mathematics in Honor of the 60th Birthday of Douglas Bridges, Chiemsee Isl, GERMANY, 19/06/06. https://doi.org/10.1002/malq.200710035","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:pure.atira.dk:publications/2415a528-e225-4e47-886a-866664f9ab31","is_oa":false,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/the-relation-reflection-scheme(2415a528-e225-4e47-886a-866664f9ab31).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aczel, P 2008, The relation reflection scheme. in Mathematical Logic Quarterly|Math. Logic Q.. vol. 54, John Wiley & Sons Ltd, pp. 5-11, Workshop on Trends in Constructive Mathematics in Honor of the 60th Birthday of Douglas Bridges, Chiemsee Isl, GERMANY, 19/06/06. https://doi.org/10.1002/malq.200710035","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:pure.atira.dk:publications/6e90eddd-f94a-49cb-990b-023c4558c6e7","is_oa":false,"landing_page_url":"http://dblp.uni-trier.de/db/journals/mlq/mlq54.html#Aczel08","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aczel, P 2008, 'The relation reflection scheme', Mathematical Logic Quarterly, vol. 54, no. 1, pp. 5-11. https://doi.org/10.1002/malq.200710035","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W77027564","https://openalex.org/W569543113","https://openalex.org/W1498439614","https://openalex.org/W1589408343","https://openalex.org/W2002542640","https://openalex.org/W2024315465"],"related_works":["https://openalex.org/W2016661762","https://openalex.org/W1574825745","https://openalex.org/W2079743999","https://openalex.org/W2741238752","https://openalex.org/W1538212383","https://openalex.org/W2008703337","https://openalex.org/W2009439044","https://openalex.org/W3197691547","https://openalex.org/W2060433450","https://openalex.org/W1511476185"],"abstract_inverted_index":{"Abstract":[0],"We":[1,81],"introduce":[2],"a":[3,22],"new":[4],"axiom":[5,40,46],"scheme":[6,20,41,57,68,87],"for":[7],"constructive":[8,32],"set":[9,27,33],"theory,":[10],"the":[11,25,31,39,45,51,56,67,86],"Relation":[12],"Reflection":[13],"Scheme":[14],"(RRS).":[15],"Each":[16],"instance":[17],"of":[18,24,47,58,75,85,91],"this":[19],"is":[21,42,53,70],"theorem":[23],"classical":[26],"theory":[28,34],"ZF.":[29],"In":[30,63],"CZF":[35,76],"\u2013":[36,77],",":[37],"when":[38],"combined":[43],"with":[44],"Dependent":[48,60],"Choices":[49,61],"(DC),":[50],"result":[52],"equivalent":[54],"to":[55,65,88],"Relative":[59],"(RDC).":[62],"contrast":[64],"RDC,":[66],"RRS":[69],"preserved":[71],"in":[72],"Heyting\u2010valued":[73],"models":[74],"using":[78],"set\u2010generated":[79],"frames.":[80],"give":[82],"an":[83],"application":[84],"coinductive":[89],"definitions":[90],"classes.":[92],"(\u00a9":[93],"2008":[94],"WILEY\u2010VCH":[95],"Verlag":[96],"GmbH":[97],"&":[98],"Co.":[99],"KGaA,":[100],"Weinheim)":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}