{"id":"https://openalex.org/W2100903326","doi":"https://doi.org/10.1017/s0022481200031248","title":"On the strength of nonstandard analysis","display_name":"On the strength of nonstandard analysis","publication_year":1986,"publication_date":"1986-06-01","ids":{"openalex":"https://openalex.org/W2100903326","doi":"https://doi.org/10.1017/s0022481200031248","mag":"2100903326"},"language":"en","primary_location":{"id":"doi:10.1017/s0022481200031248","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200031248","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal 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/A5090166557","display_name":"C. Ward Henson","orcid":"https://orcid.org/0000-0003-1499-4432"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C. Ward Henson","raw_affiliation_strings":["Department of Mathematics, University of Illinois, Urbana, Illinois 61801","Department of Mathematics, University of Illinois, Urbana, Illinois, 61801"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, Illinois 61801","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, Illinois, 61801","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009762723","display_name":"H. Jerome Keisler","orcid":"https://orcid.org/0009-0007-1747-1393"},"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":false,"raw_author_name":"H. Jerome Keisler","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706","Department of Mathematics , University of Wisconsin , Madison, Wisconsin, 53706"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Department of Mathematics , University of Wisconsin , Madison, Wisconsin, 53706","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090166557"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.5777,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.82137873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"51","issue":"2","first_page":"377","last_page":"386"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12170","display_name":"History and Theory of Mathematics","score":0.9689000248908997,"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"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9666000008583069,"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/assertion","display_name":"Assertion","score":0.9151899814605713},{"id":"https://openalex.org/keywords/confusion","display_name":"Confusion","score":0.7659280896186829},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6735751032829285},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6153795123100281},{"id":"https://openalex.org/keywords/reverse-mathematics","display_name":"Reverse mathematics","score":0.5503720641136169},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5370819568634033},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.5152483582496643},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.5119836926460266},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.4657154083251953},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4552329182624817},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3925292193889618},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3876808285713196},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3619517385959625},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28397858142852783},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2302999496459961},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.2050587236881256}],"concepts":[{"id":"https://openalex.org/C40422974","wikidata":"https://www.wikidata.org/wiki/Q741248","display_name":"Assertion","level":2,"score":0.9151899814605713},{"id":"https://openalex.org/C2781140086","wikidata":"https://www.wikidata.org/wiki/Q557945","display_name":"Confusion","level":2,"score":0.7659280896186829},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6735751032829285},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6153795123100281},{"id":"https://openalex.org/C127753061","wikidata":"https://www.wikidata.org/wiki/Q2005236","display_name":"Reverse mathematics","level":3,"score":0.5503720641136169},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5370819568634033},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.5152483582496643},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.5119836926460266},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.4657154083251953},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4552329182624817},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3925292193889618},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3876808285713196},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3619517385959625},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28397858142852783},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2302999496459961},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.2050587236881256},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C11171543","wikidata":"https://www.wikidata.org/wiki/Q41630","display_name":"Psychoanalysis","level":1,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0022481200031248","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200031248","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183742103","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183742103","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W62878982","https://openalex.org/W265040288","https://openalex.org/W1502653069","https://openalex.org/W1516893066","https://openalex.org/W1648879120","https://openalex.org/W1843935787","https://openalex.org/W1853505122","https://openalex.org/W1964095001","https://openalex.org/W1990582318","https://openalex.org/W2017398442","https://openalex.org/W2052045432","https://openalex.org/W2069787050","https://openalex.org/W2106260240","https://openalex.org/W2160331299","https://openalex.org/W2332062577","https://openalex.org/W2572301780","https://openalex.org/W2799061192"],"related_works":["https://openalex.org/W4229690001","https://openalex.org/W3109582549","https://openalex.org/W1574825745","https://openalex.org/W2367592385","https://openalex.org/W2151251236","https://openalex.org/W4237197901","https://openalex.org/W3034016151","https://openalex.org/W4210343663","https://openalex.org/W2373903136","https://openalex.org/W2951707517"],"abstract_inverted_index":{"It":[0,180],"is":[1,28,34,56,78,104,116,140,151,165],"often":[2],"asserted":[3],"in":[4,37,72,95,112,177,192,198],"the":[5,66,79,117,153,169],"literature":[6],"that":[7,31,152,188],"any":[8,83,123],"theorem":[9,84,111,124],"which":[10,42,85,125,157,173],"can":[11,17,43,69,86,92,126,132],"be":[12,19,44,51,70,87,93,127,133],"proved":[13,20,45,52,88,94,128,134],"using":[14,89,129],"nonstandard":[15,47,90,130,144],"analysis":[16,48,91,131],"also":[18],"without":[21,53,135],"it.":[22,54],"The":[23,146],"purpose":[24],"of":[25,61,155,171],"this":[26,32,149],"paper":[27],"to":[29],"show":[30],"assertion":[33,68],"wrong,":[35],"and":[36,102,137,186,205],"fact":[38],"there":[39,77,115,139],"are":[40,158,174],"theorems":[41],"with":[46,99,202],"but":[49],"cannot":[50],"There":[55],"currently":[57],"a":[58,110],"great":[59],"deal":[60],"confusion":[62,150],"among":[63],"mathematicians":[64],"because":[65],"above":[67],"interpreted":[71],"two":[73],"different":[74],"ways.":[75],"First,":[76],"following":[80],"correct":[81],"statement:":[82],"Zermelo-Fraenkel":[96],"set":[97,154,170],"theory":[98],"choice,":[100],"ZFC,":[101,164],"thus":[103,138],"acceptable":[105],"by":[106,121,160],"contemporary":[107],"standards":[108],"as":[109],"mathematics.":[113],"Second,":[114],"erroneous":[118],"conclusion":[119],"drawn":[120],"skeptics:":[122],"it,":[136],"no":[141],"need":[142],"for":[143,148],"analysis.":[145],"reason":[147],"principles":[156,172],"accepted":[159],"current":[161],"mathematics,":[162],"namely":[163],"much":[166],"stronger":[167],"than":[168],"actually":[175],"used":[176],"mathematical":[178],"practice.":[179],"has":[181],"been":[182],"observed":[183],"(see":[184],"[F]":[185],"[S])":[187],"almost":[189],"all":[190],"results":[191],"classical":[193],"mathematics":[194],"use":[195],"methods":[196],"available":[197],"second":[199],"order":[200],"arithmetic":[201],"appropriate":[203],"comprehension":[204],"choice":[206],"axiom":[207],"schemes.":[208]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}