{"id":"https://openalex.org/W3201909771","doi":"https://doi.org/10.1142/s0219061322500015","title":"Reducing \u03c9-model reflection to iterated syntactic reflection","display_name":"Reducing \u03c9-model reflection to iterated syntactic reflection","publication_year":2021,"publication_date":"2021-10-06","ids":{"openalex":"https://openalex.org/W3201909771","doi":"https://doi.org/10.1142/s0219061322500015","mag":"3201909771"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061322500015","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061322500015","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","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/A5064019679","display_name":"Fedor Pakhomov","orcid":"https://orcid.org/0000-0002-9629-9259"},"institutions":[{"id":"https://openalex.org/I2801160905","display_name":"Steklov Mathematical Institute","ror":"https://ror.org/03zeg8w71","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801160905","https://openalex.org/I4210124601"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]},{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"funder","lineage":["https://openalex.org/I1313323035"]}],"countries":["BE","RU"],"is_corresponding":true,"raw_author_name":"Fedor Pakhomov","raw_affiliation_strings":["Ghent University, Belgium, Steklov Mathematical Institute, of Russian Academy of Sciences, Russia"],"affiliations":[{"raw_affiliation_string":"Ghent University, Belgium, Steklov Mathematical Institute, of Russian Academy of Sciences, Russia","institution_ids":["https://openalex.org/I2801160905","https://openalex.org/I1313323035","https://openalex.org/I32597200"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018319982","display_name":"James Walsh","orcid":"https://orcid.org/0000-0003-0630-5617"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Walsh","raw_affiliation_strings":["Sage School of Philosophy, Cornell University, USA"],"affiliations":[{"raw_affiliation_string":"Sage School of Philosophy, Cornell University, USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064019679"],"corresponding_institution_ids":["https://openalex.org/I1313323035","https://openalex.org/I2801160905","https://openalex.org/I32597200"],"apc_list":null,"apc_paid":null,"fwci":0.3015,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62677783,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"23","issue":"02","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":0.9904000163078308,"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":0.9904000163078308,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9858999848365784,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.984000027179718,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.6877492070198059},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6196886301040649},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.5790385007858276},{"id":"https://openalex.org/keywords/reflection-principle","display_name":"Reflection principle (Wiener process)","score":0.5722804665565491},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.509522020816803},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.4273136258125305},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3660004734992981},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2235563099384308},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08932703733444214},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08365440368652344}],"concepts":[{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6877492070198059},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6196886301040649},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.5790385007858276},{"id":"https://openalex.org/C118368358","wikidata":"https://www.wikidata.org/wiki/Q7307248","display_name":"Reflection principle (Wiener process)","level":5,"score":0.5722804665565491},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.509522020816803},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.4273136258125305},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3660004734992981},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2235563099384308},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08932703733444214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08365440368652344},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.0},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.0},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"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/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0219061322500015","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061322500015","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:archive.ugent.be:8735660","is_oa":false,"landing_page_url":"http://hdl.handle.net/1854/LU-8735660","pdf_url":null,"source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1793-6691","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W144641616","https://openalex.org/W1501209070","https://openalex.org/W1980969069","https://openalex.org/W1989844562","https://openalex.org/W2005337919","https://openalex.org/W2047026488","https://openalex.org/W2058431170","https://openalex.org/W2093435953","https://openalex.org/W2094244132","https://openalex.org/W2146064316","https://openalex.org/W2155734270","https://openalex.org/W2335350341","https://openalex.org/W3106208063","https://openalex.org/W4229690001","https://openalex.org/W4256442140"],"related_works":["https://openalex.org/W2128792511","https://openalex.org/W2095873474","https://openalex.org/W2903629929","https://openalex.org/W1995092016","https://openalex.org/W4310745869","https://openalex.org/W3137360833","https://openalex.org/W4287262232","https://openalex.org/W2798507261","https://openalex.org/W1565458059","https://openalex.org/W3201909771"],"abstract_inverted_index":{"In":[0,48],"mathematical":[1],"logic":[2],"there":[3],"are":[4,97],"two":[5,56],"seemingly":[6],"distinct":[7],"kinds":[8,57],"of":[9,58,64,74,88,107,123,129,132,136,153,161,172,178],"principles":[10,16,36,60],"called":[11],"\u201creflection":[12],"principles.\u201d":[13],"Semantic":[14],"reflection":[15,35,59,79,93],"assert":[17,37],"that":[18,38,85,149],"if":[19],"a":[20,31,71,137,176],"formula":[21],"holds":[22,29],"in":[23,30,61],"the":[24,62,83,127,130,133,144,151,158,170],"whole":[25],"universe,":[26],"then":[27],"it":[28],"set-sized":[32],"model.":[33],"Syntactic":[34],"every":[39],"provable":[40,179],"sentence":[41],"from":[42],"some":[43],"complexity":[44],"class":[45],"is":[46,80,126,143],"true.":[47],"this":[49],"paper,":[50],"we":[51],"study":[52],"connections":[53],"between":[54,111],"these":[55],"setting":[63],"second-order":[65],"arithmetic.":[66],"We":[67,165],"prove":[68],"that,":[69],"for":[70,208],"large":[72],"swathe":[73],"theories,":[75],"[Formula:":[76,90,98,112,116,139,154,162,180,193,196,200],"see":[77,91,99,113,117,140,155,163,181,194,197,201],"text]-model":[78,182],"equivalent":[81],"to":[82,157,188],"claim":[84],"arbitrary":[86],"iterations":[87],"uniform":[89,104],"text]":[92,114,156,198,202],"along":[94],"countable":[95,147],"well-orderings":[96],"text]-sound.":[100],"This":[101,184],"result":[102],"yields":[103],"ordinal":[105,160],"analyzes":[106],"theories":[108],"with":[109],"strength":[110],"and":[115,199],"text].":[118,164],"The":[119],"main":[120],"technical":[121],"novelty":[122],"our":[124],"analysis":[125],"introduction":[128],"notion":[131],"proof-theoretic":[134,159,173],"dilator":[135],"theory":[138],"text],":[141,195],"which":[142],"operator":[145],"on":[146],"ordinals":[148,203],"maps":[150],"order-type":[152],"obtain":[166,190],"precise":[167],"results":[168],"about":[169],"growth":[171],"dilators":[174],"as":[175],"function":[177],"reflection.":[183],"approach":[185],"enables":[186],"us":[187],"simultaneously":[189],"not":[191],"only":[192],"but":[204],"also":[205],"reverse-mathematical":[206],"theorems":[207],"well-ordering":[209],"principles.":[210]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-03T08:47:05.690250","created_date":"2025-10-10T00:00:00"}