{"id":"https://openalex.org/W3009083242","doi":"https://doi.org/10.3233/com-180235","title":"Compositions of multivalued functions","display_name":"Compositions of multivalued functions","publication_year":2020,"publication_date":"2020-03-06","ids":{"openalex":"https://openalex.org/W3009083242","doi":"https://doi.org/10.3233/com-180235","mag":"3009083242"},"language":"en","primary_location":{"id":"doi:10.3233/com-180235","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-180235","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":"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/A5007242190","display_name":"Jun Le Goh","orcid":"https://orcid.org/0000-0002-0487-7358"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jun Le Goh","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison, Madison, WI, USA. junle.goh@wisc.edu"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, Madison, WI, USA. junle.goh@wisc.edu","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007242190"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":0.4222,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.66460375,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"9","issue":"3-4","first_page":"231","last_page":"247"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9929999709129333,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9929999709129333,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9921000003814697,"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":0.98089998960495,"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/mathematics","display_name":"Mathematics","score":0.3178694248199463}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3178694248199463}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3233/com-180235","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-180235","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:scholarbank.nus.edu.sg:10635/226817","is_oa":false,"landing_page_url":"https://scholarbank.nus.edu.sg/handle/10635/226817","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Elements","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1559786600","https://openalex.org/W1991124928","https://openalex.org/W2018837422","https://openalex.org/W2044009111","https://openalex.org/W2137505175","https://openalex.org/W2148962283","https://openalex.org/W2215415851","https://openalex.org/W2345216810","https://openalex.org/W2474654837","https://openalex.org/W2962720709","https://openalex.org/W2963469697","https://openalex.org/W2963693343","https://openalex.org/W3099840387","https://openalex.org/W3100726716","https://openalex.org/W3103464449","https://openalex.org/W3106040729","https://openalex.org/W4214815892"],"related_works":["https://openalex.org/W2044189972","https://openalex.org/W1974891317","https://openalex.org/W2313400459","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2069964982","https://openalex.org/W2007596026","https://openalex.org/W2965437270","https://openalex.org/W2061531152","https://openalex.org/W2911598644"],"abstract_inverted_index":{"In":[0],"reverse":[1],"mathematics,":[2],"one":[3,63,71],"sometimes":[4],"encounters":[5],"proofs":[6],"which":[7],"invoke":[8,16],"some":[9],"theorem":[10,29,35],"multiple":[11,78],"times":[12],"in":[13,19,84,128],"series,":[14],"or":[15],"different":[17],"theorems":[18],"series.":[20,85],"One":[21],"example":[22],"is":[23,42],"the":[24,56,68,95,98,102,107],"standard":[25],"proof":[26],"that":[27,123],"Ramsey\u2019s":[28,34],"for":[30,36,115],"2":[31],"colors":[32],"implies":[33],"3":[37],"colors.":[38],"A":[39],"natural":[40],"question":[41],"whether":[43],"such":[44],"repeated":[45],"applications":[46],"are":[47,87,125],"necessary.":[48],"Questions":[49],"like":[50],"this":[51,93],"can":[52,64],"be":[53,118],"studied":[54],"under":[55],"framework":[57],"of":[58,70,80],"Weihrauch":[59],"reducibility.":[60],"For":[61],"example,":[62],"attempt":[65],"to":[66,77,91,117],"capture":[67],"notion":[69],"multivalued":[72,82],"function":[73,83],"being":[74],"uniformly":[75],"reducible":[76],"instances":[79],"another":[81],"There":[86],"three":[88],"known":[89],"ways":[90],"formalize":[92],"notion:":[94],"compositional":[96],"product,":[97],"reduction":[99],"game,":[100],"and":[101],"step":[103],"product.":[104],"We":[105,120],"clarify":[106],"relationships":[108],"between":[109],"them":[110,116],"by":[111],"giving":[112],"sufficient":[113],"conditions":[114],"equivalent.":[119],"also":[121],"show":[122],"they":[124],"not":[126],"equivalent":[127],"general.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}