{"id":"https://openalex.org/W2563806438","doi":"https://doi.org/10.1017/s1755020316000411","title":"THE PREHISTORY OF THE SUBSYSTEMS OF SECOND-ORDER ARITHMETIC","display_name":"THE PREHISTORY OF THE SUBSYSTEMS OF SECOND-ORDER ARITHMETIC","publication_year":2017,"publication_date":"2017-02-20","ids":{"openalex":"https://openalex.org/W2563806438","doi":"https://doi.org/10.1017/s1755020316000411","mag":"2563806438"},"language":"en","primary_location":{"id":"doi:10.1017/s1755020316000411","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020316000411","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Review of Symbolic 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/A5031442931","display_name":"Walter Dean","orcid":"https://orcid.org/0000-0002-4021-5626"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"WALTER DEAN","raw_affiliation_strings":["Department of Philosophy, University of Warwick"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Philosophy, University of Warwick","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048607449","display_name":"Sean Walsh","orcid":null},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"SEAN WALSH","raw_affiliation_strings":["Department of Logic and Philosophy of Science, University of California, Irvine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Logic and Philosophy of Science, University of California, Irvine","institution_ids":["https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031442931","https://openalex.org/A5048607449"],"corresponding_institution_ids":["https://openalex.org/I204250578","https://openalex.org/I39555362"],"apc_list":null,"apc_paid":null,"fwci":6.6964,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.97321079,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"10","issue":"2","first_page":"357","last_page":"396"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9986000061035156,"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":0.9986000061035156,"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/T10778","display_name":"Philosophy and History of Science","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.8298669457435608},{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.7169485688209534},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.7003635168075562},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.628662109375},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6033972501754761},{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.5976635813713074},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.542419970035553},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46927013993263245},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.4647720456123352},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.4527370035648346},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4498792886734009},{"id":"https://openalex.org/keywords/numeral-system","display_name":"Numeral system","score":0.4436769187450409},{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.38346001505851746},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3166589140892029},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2904275059700012},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2084779441356659},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1280195713043213},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07364699244499207}],"concepts":[{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.8298669457435608},{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.7169485688209534},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.7003635168075562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.628662109375},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6033972501754761},{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.5976635813713074},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.542419970035553},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46927013993263245},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4647720456123352},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.4527370035648346},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4498792886734009},{"id":"https://openalex.org/C204160518","wikidata":"https://www.wikidata.org/wiki/Q122653","display_name":"Numeral system","level":2,"score":0.4436769187450409},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.38346001505851746},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3166589140892029},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2904275059700012},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2084779441356659},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1280195713043213},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07364699244499207},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s1755020316000411","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020316000411","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Review of Symbolic Logic","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":198,"referenced_works":["https://openalex.org/W4594304","https://openalex.org/W6754198","https://openalex.org/W45946431","https://openalex.org/W127126552","https://openalex.org/W132036571","https://openalex.org/W156955290","https://openalex.org/W167740291","https://openalex.org/W183174433","https://openalex.org/W195189594","https://openalex.org/W429991845","https://openalex.org/W561202933","https://openalex.org/W567983113","https://openalex.org/W580861338","https://openalex.org/W600072479","https://openalex.org/W610666121","https://openalex.org/W611546922","https://openalex.org/W652427957","https://openalex.org/W654727740","https://openalex.org/W805212132","https://openalex.org/W852848344","https://openalex.org/W883393071","https://openalex.org/W968348972","https://openalex.org/W986821702","https://openalex.org/W1027937706","https://openalex.org/W1028231612","https://openalex.org/W1454513529","https://openalex.org/W1456714428","https://openalex.org/W1476448305","https://openalex.org/W1483568252","https://openalex.org/W1485060831","https://openalex.org/W1486610321","https://openalex.org/W1487756945","https://openalex.org/W1491173026","https://openalex.org/W1491813684","https://openalex.org/W1493890316","https://openalex.org/W1499154644","https://openalex.org/W1506247181","https://openalex.org/W1513407571","https://openalex.org/W1513919859","https://openalex.org/W1513955923","https://openalex.org/W1522998756","https://openalex.org/W1525202879","https://openalex.org/W1534051161","https://openalex.org/W1536240750","https://openalex.org/W1538838225","https://openalex.org/W1539382740","https://openalex.org/W1539702044","https://openalex.org/W1544540238","https://openalex.org/W1545407410","https://openalex.org/W1554737135","https://openalex.org/W1554860413","https://openalex.org/W1555991696","https://openalex.org/W1556453281","https://openalex.org/W1562318894","https://openalex.org/W1565376387","https://openalex.org/W1567156820","https://openalex.org/W1569567843","https://openalex.org/W1572451808","https://openalex.org/W1579817075","https://openalex.org/W1607953571","https://openalex.org/W1886621075","https://openalex.org/W1945611796","https://openalex.org/W1960494084","https://openalex.org/W1965905187","https://openalex.org/W1975810242","https://openalex.org/W1977324591","https://openalex.org/W1978270323","https://openalex.org/W1979862983","https://openalex.org/W1979996376","https://openalex.org/W1981243252","https://openalex.org/W1982821787","https://openalex.org/W1985132925","https://openalex.org/W1986076325","https://openalex.org/W1987762167","https://openalex.org/W1988354173","https://openalex.org/W1989341191","https://openalex.org/W1990474964","https://openalex.org/W1991697528","https://openalex.org/W1996065564","https://openalex.org/W1996404651","https://openalex.org/W1996932891","https://openalex.org/W1997677910","https://openalex.org/W2004839050","https://openalex.org/W2005031151","https://openalex.org/W2005607143","https://openalex.org/W2007983321","https://openalex.org/W2025286821","https://openalex.org/W2025403483","https://openalex.org/W2027226050","https://openalex.org/W2031151986","https://openalex.org/W2031288546","https://openalex.org/W2033225733","https://openalex.org/W2038447110","https://openalex.org/W2038489218","https://openalex.org/W2041327863","https://openalex.org/W2041833446","https://openalex.org/W2049288284","https://openalex.org/W2055068568","https://openalex.org/W2060878518","https://openalex.org/W2067139650","https://openalex.org/W2067209355","https://openalex.org/W2067474877","https://openalex.org/W2067914884","https://openalex.org/W2068096743","https://openalex.org/W2071514253","https://openalex.org/W2071956244","https://openalex.org/W2074560788","https://openalex.org/W2075471377","https://openalex.org/W2081002360","https://openalex.org/W2081211885","https://openalex.org/W2082758679","https://openalex.org/W2086121436","https://openalex.org/W2087100744","https://openalex.org/W2087489880","https://openalex.org/W2087590092","https://openalex.org/W2090190027","https://openalex.org/W2092169546","https://openalex.org/W2096837500","https://openalex.org/W2102488782","https://openalex.org/W2107966045","https://openalex.org/W2108855264","https://openalex.org/W2109492210","https://openalex.org/W2114515271","https://openalex.org/W2118085624","https://openalex.org/W2118148896","https://openalex.org/W2129507111","https://openalex.org/W2137996347","https://openalex.org/W2140792783","https://openalex.org/W2143162796","https://openalex.org/W2144086150","https://openalex.org/W2150763560","https://openalex.org/W2150923863","https://openalex.org/W2162168838","https://openalex.org/W2224446306","https://openalex.org/W2241572260","https://openalex.org/W2302646607","https://openalex.org/W2320092562","https://openalex.org/W2326788312","https://openalex.org/W2329685449","https://openalex.org/W2342191445","https://openalex.org/W2403653109","https://openalex.org/W2484792804","https://openalex.org/W2487893106","https://openalex.org/W2493479077","https://openalex.org/W2494939278","https://openalex.org/W2496540450","https://openalex.org/W2583443307","https://openalex.org/W2735780516","https://openalex.org/W2736186402","https://openalex.org/W2917866299","https://openalex.org/W2977904728","https://openalex.org/W3000593863","https://openalex.org/W3038873949","https://openalex.org/W3046397786","https://openalex.org/W3096960498","https://openalex.org/W3120173222","https://openalex.org/W3131590544","https://openalex.org/W3149024532","https://openalex.org/W3156385722","https://openalex.org/W3159698340","https://openalex.org/W3210382447","https://openalex.org/W4210953275","https://openalex.org/W4214648487","https://openalex.org/W4229636845","https://openalex.org/W4229690001","https://openalex.org/W4232166111","https://openalex.org/W4233662453","https://openalex.org/W4234232942","https://openalex.org/W4234684401","https://openalex.org/W4234966326","https://openalex.org/W4236364473","https://openalex.org/W4237609772","https://openalex.org/W4238103299","https://openalex.org/W4239934161","https://openalex.org/W4240740245","https://openalex.org/W4242304899","https://openalex.org/W4243483475","https://openalex.org/W4244401852","https://openalex.org/W4246326106","https://openalex.org/W4249355983","https://openalex.org/W4252024908","https://openalex.org/W4252521283","https://openalex.org/W4254994720","https://openalex.org/W4255494769","https://openalex.org/W4296119740","https://openalex.org/W4296611970","https://openalex.org/W4300876653","https://openalex.org/W4388156054","https://openalex.org/W4388254626","https://openalex.org/W6616838144","https://openalex.org/W6633401074","https://openalex.org/W6640645558","https://openalex.org/W6658831528","https://openalex.org/W6662901914","https://openalex.org/W6677258542","https://openalex.org/W6697698534","https://openalex.org/W6741189996","https://openalex.org/W6794424659"],"related_works":["https://openalex.org/W4235932242","https://openalex.org/W2025460262","https://openalex.org/W1616114834","https://openalex.org/W1537958706","https://openalex.org/W4200573286","https://openalex.org/W4311117965","https://openalex.org/W3037940532","https://openalex.org/W2008203175","https://openalex.org/W4226435082","https://openalex.org/W2101785868"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"presents":[3],"a":[4],"systematic":[5],"study":[6],"of":[7,10,14,57,65,77],"the":[8,11,21,36,50,55,60,70,74,86],"prehistory":[9],"traditional":[12],"subsystems":[13],"second-order":[15],"arithmetic":[16,45],"that":[17],"feature":[18],"prominently":[19],"in":[20,32,59,94],"reverse":[22],"mathematics":[23],"program":[24],"promoted":[25],"by":[26,101],"Friedman":[27],"and":[28,47,54,63,67,84,98,105],"Simpson.":[29],"We":[30],"look":[31],"particular":[33],"at:":[34],"(i)":[35],"long":[37],"arc":[38],"from":[39],"Poincar\u00e9":[40],"to":[41,73,80,90],"Feferman":[42],"as":[43,72],"concerns":[44],"definability":[46],"provability,":[48],"(ii)":[49],"interplay":[51],"between":[52],"finitism":[53],"formalization":[56],"analysis":[58],"lecture":[61],"notes":[62],"publications":[64],"Hilbert":[66],"Bernays,":[68],"(iii)":[69],"uncertainty":[71],"constructive":[75],"status":[76],"principles":[78],"equivalent":[79],"Weak":[81],"K\u00f6nig\u2019s":[82],"Lemma,":[83],"(iv)":[85],"large-scale":[87],"intellectual":[88],"backdrop":[89],"arithmetical":[91],"transfinite":[92],"recursion":[93],"descriptive":[95],"set":[96],"theory":[97],"its":[99],"effectivization":[100],"Borel,":[102],"Lusin,":[103],"Addison,":[104],"others.":[106]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":23}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
