{"id":"https://openalex.org/W4400703282","doi":"https://doi.org/10.1093/jigpal/jzae130","title":"Boundedly finite-to-one functions","display_name":"Boundedly finite-to-one functions","publication_year":2024,"publication_date":"2024-12-21","ids":{"openalex":"https://openalex.org/W4400703282","doi":"https://doi.org/10.1093/jigpal/jzae130"},"language":"en","primary_location":{"id":"doi:10.1093/jigpal/jzae130","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzae130","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2407.10183","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Xiao Hu","orcid":null},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao Hu","raw_affiliation_strings":["School of Philosophy , Wuhan University, No. 299 Bayi Road, Wuhan, Hubei Province 430072, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Philosophy , Wuhan University, No. 299 Bayi Road, Wuhan, Hubei Province 430072, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5104621392","display_name":"Guozhen Shen","orcid":null},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guozhen Shen","raw_affiliation_strings":["School of Philosophy , Wuhan University, No. 299 Bayi Road, Wuhan, Hubei Province 430072, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Philosophy , Wuhan University, No. 299 Bayi Road, Wuhan, Hubei Province 430072, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I37461747"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11720418,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.5809999704360962,"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":0.5809999704360962,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.522599995136261,"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":0.4787999987602234,"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/mathematical-economics","display_name":"Mathematical economics","score":0.3934897184371948},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3728719651699066},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3549700677394867}],"concepts":[{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3934897184371948},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3728719651699066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3549700677394867}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1093/jigpal/jzae130","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzae130","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2407.10183","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2407.10183","pdf_url":"https://arxiv.org/pdf/2407.10183","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2407.10183","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2407.10183","pdf_url":"https://arxiv.org/pdf/2407.10183","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4001432382","display_name":null,"funder_award_id":"12101466","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400703282.pdf","grobid_xml":"https://content.openalex.org/works/W4400703282.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W945849841","https://openalex.org/W2071343329","https://openalex.org/W2078762661","https://openalex.org/W2161061660","https://openalex.org/W2342191445","https://openalex.org/W2880168949","https://openalex.org/W2984799802","https://openalex.org/W2985622622","https://openalex.org/W4230632233","https://openalex.org/W4283312226","https://openalex.org/W4287218097","https://openalex.org/W4385584298","https://openalex.org/W4393862295","https://openalex.org/W6859431842"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"function":[2,64,107],"is":[3,8,60,72,83,103,114,126,130],"boundedly":[4,62,105],"finite-to-one":[5,63,106],"if":[6],"there":[7,59,102],"a":[9],"natural":[10,56],"number":[11,57],"$k$":[12,20],"such":[13,122],"that":[14,123],"each":[15,51,98],"point":[16],"has":[17],"at":[18,92],"most":[19,93],"inverse":[21],"images.":[22],"In":[23],"this":[24,43],"paper,":[25],"we":[26],"prove":[27],"in":[28],"$\\textsf{ZF}$":[29],"(i.e.":[30],"the":[31,36,48,73,84,115,131],"Zermelo\u2013Fraenkel":[32],"set":[33,53,74,85,100,116,132],"theory":[34],"without":[35],"axiom":[37],"of":[38,75,78,86,89,117,120,133,137],"choice)":[39],"several":[40],"results":[41],"concerning":[42],"notion,":[44],"among":[45],"which":[46],"are":[47],"following:":[49],"(1)For":[50],"infinite":[52,99],"$A$":[54,79,90,121],"and":[55,80,128],"$n$,":[58],"no":[61,104],"from":[65,108],"$\\mathcal{S}(A)$":[66,71],"to":[67,110],"$\\mathcal{S}_{\\leq":[68,81],"n}(A)$,":[69],"where":[70,112],"all":[76,87,118,134],"permutations":[77,88],"n}(A)$":[82],"moving":[91],"$n$":[94],"points.":[95],"(2)":[96],"For":[97],"$A$,":[101],"$\\mathcal{B}(A)$":[109,113],"$\\textrm{fin}(A)$,":[111],"partitions":[119],"every":[124],"block":[125],"finite":[127,135],"$\\textrm{fin}(A)$":[129],"subsets":[136],"$A$.":[138]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}