{"id":"https://openalex.org/W4381884567","doi":"https://doi.org/10.3233/com-170176","title":"Limit computability and ultrafilters","display_name":"Limit computability and ultrafilters","publication_year":2023,"publication_date":"2023-06-21","ids":{"openalex":"https://openalex.org/W4381884567","doi":"https://doi.org/10.3233/com-170176"},"language":"en","primary_location":{"id":"doi:10.3233/com-170176","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-170176","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/A5022967955","display_name":"Uri Andrews","orcid":"https://orcid.org/0000-0002-4653-7458"},"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":"Uri Andrews","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, 213 Van Vleck Hall, Madison, WI 53706, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, 213 Van Vleck Hall, Madison, WI 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070121269","display_name":"Mingzhong Cai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mingzhong Cai","raw_affiliation_strings":["Hyperimmune Books, 620 Morning Creek Ln, Suwanee, GA 30024, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hyperimmune Books, 620 Morning Creek Ln, Suwanee, GA 30024, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070121269","display_name":"Mingzhong Cai","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mingzhong Cai","raw_affiliation_strings":["Hyperimmune Books, 620 Morning Creek Ln, Suwanee, GA 30024, USA","Google, 1600 Amphitheatre Pkwy, Mountain View, CA 94043, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hyperimmune Books, 620 Morning Creek Ln, Suwanee, GA 30024, USA","institution_ids":[]},{"raw_affiliation_string":"Google, 1600 Amphitheatre Pkwy, Mountain View, CA 94043, USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047345771","display_name":"David Diamondstone","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]},{"id":"https://openalex.org/I4210127373","display_name":"Highland Community College - Illinois","ror":"https://ror.org/02mxywv89","country_code":"US","type":"education","lineage":["https://openalex.org/I4210127373"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David Diamondstone","raw_affiliation_strings":["Google, 1600 Amphitheatre Pkwy, Mountain View, CA 94043, USA","Proof School, 515 Highland Ave., San Mateo, CA 94401, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google, 1600 Amphitheatre Pkwy, Mountain View, CA 94043, USA","institution_ids":["https://openalex.org/I1291425158"]},{"raw_affiliation_string":"Proof School, 515 Highland Ave., San Mateo, CA 94401, USA","institution_ids":["https://openalex.org/I4210127373"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047345771","display_name":"David Diamondstone","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Diamondstone","raw_affiliation_strings":["Google, 1600 Amphitheatre Pkwy, Mountain View, CA 94043, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google, 1600 Amphitheatre Pkwy, Mountain View, CA 94043, USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048208997","display_name":"Noah Schweber","orcid":"https://orcid.org/0000-0001-5631-615X"},"institutions":[{"id":"https://openalex.org/I4210127373","display_name":"Highland Community College - Illinois","ror":"https://ror.org/02mxywv89","country_code":"US","type":"education","lineage":["https://openalex.org/I4210127373"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Noah Schweber","raw_affiliation_strings":["Proof School, 515 Highland Ave., San Mateo, CA 94401, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Proof School, 515 Highland Ave., San Mateo, CA 94401, USA","institution_ids":["https://openalex.org/I4210127373"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048208997","display_name":"Noah Schweber","orcid":"https://orcid.org/0000-0001-5631-615X"},"institutions":[{"id":"https://openalex.org/I4210127373","display_name":"Highland Community College - Illinois","ror":"https://ror.org/02mxywv89","country_code":"US","type":"education","lineage":["https://openalex.org/I4210127373"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Noah Schweber","raw_affiliation_strings":["Proof School, 515 Highland Ave., San Mateo, CA 94401, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Proof School, 515 Highland Ave., San Mateo, CA 94401, USA","institution_ids":["https://openalex.org/I4210127373"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022967955","https://openalex.org/A5047345771","https://openalex.org/A5048208997","https://openalex.org/A5070121269"],"corresponding_institution_ids":["https://openalex.org/I1291425158","https://openalex.org/I135310074","https://openalex.org/I4210127373"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13032467,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"2","first_page":"101","last_page":"115"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":1.0,"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":1.0,"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":0.9933000206947327,"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/T11567","display_name":"semigroups and automata theory","score":0.9901999831199646,"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/ultrafilter","display_name":"Ultrafilter","score":0.9586726427078247},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.7119745016098022},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.7025864124298096},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6960681080818176},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.659721851348877},{"id":"https://openalex.org/keywords/fubinis-theorem","display_name":"Fubini's theorem","score":0.6309410333633423},{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.5778862237930298},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5357455611228943},{"id":"https://openalex.org/keywords/reverse-mathematics","display_name":"Reverse mathematics","score":0.5310049057006836},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4789472222328186},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4772219955921173},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.45782431960105896},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.45628082752227783},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.4417506158351898},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42806410789489746},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4155064821243286},{"id":"https://openalex.org/keywords/computability-theory","display_name":"Computability theory","score":0.41132399439811707},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29052993655204773},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.12859779596328735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12296348810195923},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0832732617855072}],"concepts":[{"id":"https://openalex.org/C87598191","wikidata":"https://www.wikidata.org/wiki/Q1571831","display_name":"Ultrafilter","level":2,"score":0.9586726427078247},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.7119745016098022},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.7025864124298096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6960681080818176},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.659721851348877},{"id":"https://openalex.org/C55526981","wikidata":"https://www.wikidata.org/wiki/Q1149022","display_name":"Fubini's theorem","level":2,"score":0.6309410333633423},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.5778862237930298},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5357455611228943},{"id":"https://openalex.org/C127753061","wikidata":"https://www.wikidata.org/wiki/Q2005236","display_name":"Reverse mathematics","level":3,"score":0.5310049057006836},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4789472222328186},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4772219955921173},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.45782431960105896},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.45628082752227783},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.4417506158351898},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42806410789489746},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4155064821243286},{"id":"https://openalex.org/C111142201","wikidata":"https://www.wikidata.org/wiki/Q818930","display_name":"Computability theory","level":2,"score":0.41132399439811707},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29052993655204773},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.12859779596328735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12296348810195923},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0832732617855072},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/com-170176","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-170176","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W111470806","https://openalex.org/W1556453281","https://openalex.org/W1574049752","https://openalex.org/W4232277851"],"related_works":["https://openalex.org/W2952397345","https://openalex.org/W2167408243","https://openalex.org/W1986962265","https://openalex.org/W4248353912","https://openalex.org/W2138038016","https://openalex.org/W4253715132","https://openalex.org/W1522372633","https://openalex.org/W582328946","https://openalex.org/W1559682655","https://openalex.org/W4381884567"],"abstract_inverted_index":{"We":[0,23,179,256],"study":[1,218],"a":[2,18,27,38,95,116,159,237],"class":[3],"of":[4,29,37,128,185,189,224,254],"operators":[5],"on":[6,21,196,221,240],"Turing":[7,63,96],"degrees":[8,198,208],"arising":[9,226],"naturally":[10],"from":[11,227],"ultrafilters.":[12,255],"Suppose":[13],"[Formula:":[14,31,45,49,54,67,71,90,99,111,120,155,164,172,176,193,230],"see":[15,32,46,50,55,68,72,91,100,112,121,156,165,173,177,194,231],"text]":[16,33,47,73,92,113,157,174,195],"is":[17,93,114,139,148,158,169,247],"nonprincipal":[19],"ultrafilter":[20,171,191,214],"\u03c9.":[22],"can":[24,58],"then":[25,167,180],"view":[26],"sequence":[28],"sets":[30],"as":[34],"an":[35,125,190],"\u201capproximation\u201d":[36],"set":[39,53,118,162,223,242],"B":[40],"produced":[41],"by":[42,65,258],"amalgamating":[43],"the":[44,62,129,150,183,187,219,222,228,250],"via":[48],"text]:":[51],"we":[52,76,217,235],"text].":[56,69,101,122,178],"This":[57],"be":[59],"extended":[60],"to":[61,108,182],"degrees,":[64],"defining":[66],"The":[70],"\u2013":[74,80],"which":[75,209],"call":[77],"\u201cultrafilter":[78],"jumps\u201d":[79],"resemble":[81],"classical":[82,251],"limit":[83],"computability":[84],"in":[85,132,233],"certain":[86],"ways.":[87],"In":[88],"particular,":[89,234],"always":[94,115],"ideal":[97],"containing":[98,119,163],"However,":[102],"they":[103],"are":[104,206,210],"also":[105,152],"closely":[106],"tied":[107],"Scott":[109,117,161],"sets:":[110],"(This":[123],"yields":[124],"alternate":[126],"proof":[127],"standard":[130],"result":[131,147],"reverse":[133],"mathematics":[134],"that":[135,149,204,245],"Weak":[136],"Konig\u2019s":[137],"Lemma":[138],"strictly":[140],"weaker":[141],"than":[142],"arithmetic":[143],"comprehension.)":[144],"Our":[145],"main":[146],"converse":[151],"holds:":[153],"if":[154],"countable":[160],"text],":[166],"there":[168,205],"some":[170,213],"with":[175,249],"turn":[181],"problem":[184],"controlling":[186],"action":[188],"jump":[192],"two":[197,260],"simultaneously,":[199],"and":[200,243],"for":[201,212,262],"example":[202],"show":[203,244],"nontrivial":[207],"\u201clow\u201d":[211],"jump.":[215],"Finally,":[216],"structure":[220],"ultrafilters":[225],"construction":[229],"text];":[232],"introduce":[236],"natural":[238],"preordering":[239],"this":[241],"it":[246],"connected":[248],"Rudin\u2013Keisler":[252],"ordering":[253],"end":[257],"presenting":[259],"directions":[261],"further":[263],"research.":[264]},"counts_by_year":[],"updated_date":"2026-07-14T08:27:34.040176","created_date":"2025-10-10T00:00:00"}
