{"id":"https://openalex.org/W1981484178","doi":"https://doi.org/10.1112/s1461157000000267","title":"Mechanizing Nonstandard Real Analysis","display_name":"Mechanizing Nonstandard Real Analysis","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1981484178","doi":"https://doi.org/10.1112/s1461157000000267","mag":"1981484178"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157000000267","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000267","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1A4325EE3C91A18EF68D55407D184FB/S1461157000000267a.pdf/div-class-title-mechanizing-nonstandard-real-analysis-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1A4325EE3C91A18EF68D55407D184FB/S1461157000000267a.pdf/div-class-title-mechanizing-nonstandard-real-analysis-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026577518","display_name":"Jacques Fleuriot","orcid":"https://orcid.org/0000-0002-6867-9836"},"institutions":[{"id":"https://openalex.org/I4210127517","display_name":"Institute for Law and Justice","ror":"https://ror.org/03mn4jv82","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210127517"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB","US"],"is_corresponding":true,"raw_author_name":"Jacques D. Fleuriot","raw_affiliation_strings":["Institute for Representation and Reasoning, Division of Informatics, University of Edinburgh","Institute for Representation and Reasoning"],"affiliations":[{"raw_affiliation_string":"Institute for Representation and Reasoning, Division of Informatics, University of Edinburgh","institution_ids":["https://openalex.org/I98677209"]},{"raw_affiliation_string":"Institute for Representation and Reasoning","institution_ids":["https://openalex.org/I4210127517"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086565312","display_name":"Lawrence C. Paulson","orcid":"https://orcid.org/0000-0003-0288-4279"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Lawrence C. Paulson","raw_affiliation_strings":["Computer Laboratory, University of Cambridge","University of Cambridge,"],"affiliations":[{"raw_affiliation_string":"Computer Laboratory, University of Cambridge","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"University of Cambridge,","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026577518"],"corresponding_institution_ids":["https://openalex.org/I4210127517","https://openalex.org/I98677209"],"apc_list":null,"apc_paid":null,"fwci":1.0276,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.71741382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"3","issue":null,"first_page":"140","last_page":"190"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9986000061035156,"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":0.9986000061035156,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9923999905586243,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9815000295639038,"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/hol","display_name":"HOL","score":0.6546032428741455},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6471630334854126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6195308566093445},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.5889006853103638},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5281410217285156},{"id":"https://openalex.org/keywords/infinitesimal","display_name":"Infinitesimal","score":0.5015988349914551},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.4893345236778259},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.48042893409729004},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4500218331813812},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.39606887102127075},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39480966329574585},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3469359874725342},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3292044997215271},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3208697438240051},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2164509892463684}],"concepts":[{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.6546032428741455},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6471630334854126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6195308566093445},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.5889006853103638},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5281410217285156},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.5015988349914551},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.4893345236778259},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.48042893409729004},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4500218331813812},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.39606887102127075},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39480966329574585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3469359874725342},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3292044997215271},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3208697438240051},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2164509892463684},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1112/s1461157000000267","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000267","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1A4325EE3C91A18EF68D55407D184FB/S1461157000000267a.pdf/div-class-title-mechanizing-nonstandard-real-analysis-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1112/s1461157000000267","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000267","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1A4325EE3C91A18EF68D55407D184FB/S1461157000000267a.pdf/div-class-title-mechanizing-nonstandard-real-analysis-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1981484178.pdf","grobid_xml":"https://content.openalex.org/works/W1981484178.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W66289639","https://openalex.org/W566121181","https://openalex.org/W1502653069","https://openalex.org/W1509211745","https://openalex.org/W1521083034","https://openalex.org/W1525108918","https://openalex.org/W1550809037","https://openalex.org/W1561578951","https://openalex.org/W1584275176","https://openalex.org/W1586167239","https://openalex.org/W1595814451","https://openalex.org/W1601195943","https://openalex.org/W1994615143","https://openalex.org/W1996404651","https://openalex.org/W1998146115","https://openalex.org/W2022261955","https://openalex.org/W2052995997","https://openalex.org/W2070257340","https://openalex.org/W2072405721","https://openalex.org/W2073127449","https://openalex.org/W2073518297","https://openalex.org/W2080104522","https://openalex.org/W2097663235","https://openalex.org/W2133126578","https://openalex.org/W2168796774","https://openalex.org/W2261622378","https://openalex.org/W2487666141","https://openalex.org/W2499957903","https://openalex.org/W2895656663","https://openalex.org/W2951707517","https://openalex.org/W3013219702","https://openalex.org/W3037057000","https://openalex.org/W3162919972","https://openalex.org/W6764663946"],"related_works":["https://openalex.org/W4293192252","https://openalex.org/W1679173830","https://openalex.org/W4313389715","https://openalex.org/W3084111828","https://openalex.org/W1520750303","https://openalex.org/W3200122939","https://openalex.org/W2175970794","https://openalex.org/W2945435258","https://openalex.org/W2755403568","https://openalex.org/W1981484178"],"abstract_inverted_index":{"Abstract":[0],"This":[1,123],"paper":[2,124],"first":[3],"describes":[4,126],"the":[5,10,13,17,34,50,60,67,76,85,88,97,100,119,127,130,156,180,185,190,196,206],"construction":[6,48,77],"and":[7,28,87,109,111,135,152,159,175,200],"use":[8,61,128],"of":[9,19,49,62,69,107,118,121,129,133,189,198],"hyperreals":[11,98],"in":[12,42,71,163,184],"theorem-prover":[14],"Isabelle":[15,72],"within":[16],"framework":[18],"higher-order":[20],"logic":[21],"(HOL).":[22],"The":[23,47,146,187],"theory,":[24],"which":[25,173],"includes":[26],"infinitesimals":[27],"infinite":[29],"numbers,":[30],"is":[31],"based":[32],"on":[33,138],"hyperreal":[35,51],"number":[36,52,82],"system":[37,53],"developed":[38,183],"by":[39],"Abraham":[40],"Robinson":[41],"his":[43],"nonstandard":[44,153,191],"analysis":[45,199],"(NSA).":[46],"has":[54,78,102],"been":[55],"carried":[56],"out":[57],"strictly":[58],"through":[59,172],"definitions":[63,154],"to":[64,95,140,179,195],"ensure":[65],"that":[66,80],"foundations":[68],"NSA":[70],"are":[73,177,182,203],"sound.":[74],"Mechanizing":[75],"required":[79,103],"various":[81,157],"systems":[83],"including":[84],"rationals":[86],"reals":[89,101],"be":[90],"built":[91],"up":[92],"first.":[93],"Moreover,":[94],"construct":[96],"from":[99,144],"developing":[104],"a":[105],"theory":[106],"filters":[108],"ultrafilters":[110],"proving":[112],"Zorn's":[113],"lemma,":[114],"an":[115],"equivalent":[116],"form":[117],"axiom":[120],"choice.":[122],"also":[125],"new":[131,136],"types":[132],"numbers":[134],"relations":[137],"them":[139],"formalize":[141],"familiar":[142],"concepts":[143],"analysis.":[145],"current":[147],"work":[148],"provides":[149],"both":[150],"standard":[151],"for":[155],"notions,":[158],"proves":[160],"their":[161],"equivalence":[162],"each":[164],"case.":[165],"To":[166],"achieve":[167],"this":[168],"aim,":[169],"systematic":[170],"methods,":[171],"sets":[174],"functions":[176],"extended":[178],"hyperreals,":[181],"framework.":[186],"merits":[188],"approach":[192],"with":[193],"respect":[194],"practice":[197],"mechanical":[201],"theorem-proving":[202],"highlighted":[204],"throughout":[205],"exposition.":[207]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}