{"id":"https://openalex.org/W2434215324","doi":"https://doi.org/10.4204/eptcs.213.3","title":"The computational content of Nonstandard Analysis","display_name":"The computational content of Nonstandard Analysis","publication_year":2016,"publication_date":"2016-06-19","ids":{"openalex":"https://openalex.org/W2434215324","doi":"https://doi.org/10.4204/eptcs.213.3","mag":"2434215324"},"language":"en","primary_location":{"id":"doi:10.4204/eptcs.213.3","is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.213.3","pdf_url":"https://arxiv.org/pdf/1606.06386","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Proceedings in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://arxiv.org/pdf/1606.06386","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Sam Sanders","orcid":null},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE","DE"],"is_corresponding":true,"raw_author_name":"Sam Sanders","raw_affiliation_strings":["LMU Munich and Ghent University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMU Munich and Ghent University","institution_ids":["https://openalex.org/I32597200","https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I32597200","https://openalex.org/I8204097"],"apc_list":null,"apc_paid":null,"fwci":0.3605,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66883079,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"213","issue":null,"first_page":"24","last_page":"40"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.41190001368522644,"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":0.41190001368522644,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.30230000615119934,"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/T10126","display_name":"Logic, programming, and type systems","score":0.1404999941587448,"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/scope","display_name":"Scope (computer science)","score":0.7720999717712402},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.7177000045776367},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.47519999742507935},{"id":"https://openalex.org/keywords/content","display_name":"Content (measure theory)","score":0.4706000089645386},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.44190001487731934},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.3952000141143799},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33329999446868896}],"concepts":[{"id":"https://openalex.org/C2778012447","wikidata":"https://www.wikidata.org/wiki/Q1034415","display_name":"Scope (computer science)","level":2,"score":0.7720999717712402},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.7177000045776367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.539900004863739},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.47519999742507935},{"id":"https://openalex.org/C2778152352","wikidata":"https://www.wikidata.org/wiki/Q5165061","display_name":"Content (measure theory)","level":2,"score":0.4706000089645386},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.44190001487731934},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.3952000141143799},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3853999972343445},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37389999628067017},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3531000018119812},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3206999897956848},{"id":"https://openalex.org/C195807954","wikidata":"https://www.wikidata.org/wiki/Q1662562","display_name":"Information extraction","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C124978682","wikidata":"https://www.wikidata.org/wiki/Q1201019","display_name":"Proof of concept","level":2,"score":0.2556000053882599},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2513999938964844}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.4204/eptcs.213.3","is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.213.3","pdf_url":"https://arxiv.org/pdf/1606.06386","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Proceedings in Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1606.06386","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.06386","pdf_url":"https://arxiv.org/pdf/1606.06386","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:archive.ugent.be:8729217","is_oa":true,"landing_page_url":"https://biblio.ugent.be/publication/8729217","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ELECTRONIC PROCEEDINGS IN THEORETICAL COMPUTER SCIENCE","raw_type":"journalArticle"},{"id":"pmh:oai:doaj.org/article:674d92f261fa441f99aa68348d1fadef","is_oa":true,"landing_page_url":"https://doaj.org/article/674d92f261fa441f99aa68348d1fadef","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Proceedings in Theoretical Computer Science, Vol 213, Iss Proc. CL&C 2016, Pp 24-40 (2016)","raw_type":"article"},{"id":"pmh:oai:epub.ub.uni-muenchen.de:38167","is_oa":false,"landing_page_url":"https://epub.ub.uni-muenchen.de/38167/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401845","display_name":"Open access LMU (Ludwid Maxmilian's Universitat Munchen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8204097","host_organization_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","host_organization_lineage":["https://openalex.org/I8204097"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Proceedings in Theoretical Computer Science","raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.4204/eptcs.213.3","is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.213.3","pdf_url":"https://arxiv.org/pdf/1606.06386","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Proceedings in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306193","display_name":"John Templeton Foundation","ror":"https://ror.org/035tnyy05"},{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320323260","display_name":"Universitetet i Oslo","ror":"https://ror.org/01xtthb56"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2434215324.pdf","grobid_xml":"https://content.openalex.org/works/W2434215324.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W561202933","https://openalex.org/W1485672136","https://openalex.org/W1516893066","https://openalex.org/W1568238685","https://openalex.org/W1580437847","https://openalex.org/W1592481455","https://openalex.org/W1653897855","https://openalex.org/W1973799827","https://openalex.org/W1974355866","https://openalex.org/W1977707014","https://openalex.org/W1996532779","https://openalex.org/W2000131152","https://openalex.org/W2026887331","https://openalex.org/W2038627458","https://openalex.org/W2042580732","https://openalex.org/W2045199616","https://openalex.org/W2045383980","https://openalex.org/W2062834538","https://openalex.org/W2065855006","https://openalex.org/W2087429103","https://openalex.org/W2094306267","https://openalex.org/W2099102402","https://openalex.org/W2111656596","https://openalex.org/W2128167204","https://openalex.org/W2132134695","https://openalex.org/W2137023255","https://openalex.org/W2170311001","https://openalex.org/W2189582351","https://openalex.org/W2249870146","https://openalex.org/W2293460502","https://openalex.org/W2593449741","https://openalex.org/W3098373946","https://openalex.org/W3207033221","https://openalex.org/W4229690001","https://openalex.org/W4237529852","https://openalex.org/W4239316923","https://openalex.org/W4247383336"],"related_works":[],"abstract_inverted_index":{"Kohlenbach's":[0],"proof":[1,31,72],"mining":[2,16,32,73],"program":[3],"deals":[4],"with":[5],"the":[6,25,43,54,71,107],"extraction":[7],"of":[8,28,33,45,56,74,94],"effective":[9],"information":[10],"from":[11,53],"typically":[12],"ineffective":[13],"proofs.":[14,29],"Proof":[15],"has":[17,78],"its":[18],"roots":[19],"in":[20,39,118],"Kreisel's":[21],"pioneering":[22],"work":[23],"on":[24],"so-called":[26],"unwinding":[27],"The":[30],"classical":[34,75],"mathematics":[35],"is":[36],"rather":[37],"restricted":[38],"scope":[40,90],"due":[41],"to":[42],"existence":[44],"sentences":[46],"without":[47],"computational":[48],"content":[49],"which":[50,60],"are":[51,110],"provable":[52],"law":[55],"excluded":[57],"middle":[58],"and":[59,122],"involve":[61],"only":[62,102],"two":[63],"quantifier":[64],"alternations.":[65],"By":[66],"contrast,":[67],"we":[68,85,115],"show":[69],"that":[70,88,101],"Nonstandard":[76,96],"Analysis":[77],"a":[79],"very":[80],"large":[81],"scope.":[82],"In":[83,112],"particular,":[84],"will":[86],"observe":[87],"this":[89,113],"includes":[91],"any":[92],"theorem":[93],"pure":[95],"Analysis,":[97],"where":[98],"`pure'":[99],"means":[100],"nonstandard":[103],"definitions":[104],"(and":[105],"not":[106],"epsilon-delta":[108],"kind)":[109],"used.":[111],"note,":[114],"survey":[116],"results":[117],"analysis,":[119],"computability":[120],"theory,":[121],"Reverse":[123],"Mathematics.":[124]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2016-06-24T00:00:00"}