ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS

ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS

We show that there is a strong connection between Weihrauch reducibility on one hand, and provability in EL₀, the intuitionistic version of RCA₀, on the other hand. More precisely, we show that Weihrauch reducibility to the composition of finitely many instances of a theorem is captured by provabili...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:The Journal of symbolic logic 2017-12, Vol.82 (4), p.1438-1458
1. Verfasser: KUYPER, RUTGER
Format: Artikel
Sprache:eng
Schlagworte:
Calculus
Mathematics
Theorems
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 1458
container_issue 4
container_start_page 1438
container_title The Journal of symbolic logic
container_volume 82
creator KUYPER, RUTGER
description We show that there is a strong connection between Weihrauch reducibility on one hand, and provability in EL₀, the intuitionistic version of RCA₀, on the other hand. More precisely, we show that Weihrauch reducibility to the composition of finitely many instances of a theorem is captured by provability in EL₀ together with Markov’s principle, and that Weihrauch reducibility is captured by an affine subsystem of EL₀ plus Markov’s principle.
doi_str_mv 10.1017/jsl.2016.61
format Article
fullrecord <record><control><sourceid>jstor_proqu</sourceid><recordid>TN_cdi_proquest_journals_2787301926</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>26600293</jstor_id><sourcerecordid>26600293</sourcerecordid><originalsourceid>FETCH-LOGICAL-c349t-49ad78537b4d0d2f5df7ace769d5f073e980ddec5fc4e934aa2d134153d72d6f3</originalsourceid><addsrcrecordid>eNo9kEtLw0AUhQdRsFZXroWAS0md92NnTKMZqCm0ieJqiJkJGKrRmXbhv3dKxc09i_txDnwAXCI4QxCJ2yFsZhgiPuPoCEyQoiRlUvJjMIEQ45RKhE_BWQgDhJApKifgblklL4UuV1mTl8mqmDe5vtcLXb8mWTVPdFU3utbLSq9rncf_c7FaF8lTVpdFPDpfn4OTvt0Ed_GXU9A8FHVepovlo86zRdoRqrYpVa0VkhHxRi20uGe2F23nBFeW9VAQpyS01nWs76hThLYttohQxIgV2PKeTMH1offLj987F7ZmGHf-M04aLKQgECnMI3VzoDo_huBdb778-0frfwyCZq_IREVmr8hwFOmrAz2E7ej_Ucx51KUI-QUipVzu</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2787301926</pqid></control><display><type>article</type><title>ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS</title><source>JSTOR Mathematics &amp; Statistics</source><source>JSTOR Archive Collection A-Z Listing</source><source>Cambridge University Press Journals Complete</source><creator>KUYPER, RUTGER</creator><creatorcontrib>KUYPER, RUTGER</creatorcontrib><description>We show that there is a strong connection between Weihrauch reducibility on one hand, and provability in EL₀, the intuitionistic version of RCA₀, on the other hand. More precisely, we show that Weihrauch reducibility to the composition of finitely many instances of a theorem is captured by provability in EL₀ together with Markov’s principle, and that Weihrauch reducibility is captured by an affine subsystem of EL₀ plus Markov’s principle.</description><identifier>ISSN: 0022-4812</identifier><identifier>EISSN: 1943-5886</identifier><identifier>DOI: 10.1017/jsl.2016.61</identifier><language>eng</language><publisher>Pasadena: Association for Symbolic Logic, Inc</publisher><subject>Calculus ; Mathematics ; Theorems</subject><ispartof>The Journal of symbolic logic, 2017-12, Vol.82 (4), p.1438-1458</ispartof><rights>2017, Association for Symbolic Logic</rights><rights>Copyright © The Association for Symbolic Logic 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c349t-49ad78537b4d0d2f5df7ace769d5f073e980ddec5fc4e934aa2d134153d72d6f3</citedby><cites>FETCH-LOGICAL-c349t-49ad78537b4d0d2f5df7ace769d5f073e980ddec5fc4e934aa2d134153d72d6f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/26600293$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/26600293$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27924,27925,58017,58021,58250,58254</link.rule.ids></links><search><creatorcontrib>KUYPER, RUTGER</creatorcontrib><title>ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS</title><title>The Journal of symbolic logic</title><description>We show that there is a strong connection between Weihrauch reducibility on one hand, and provability in EL₀, the intuitionistic version of RCA₀, on the other hand. More precisely, we show that Weihrauch reducibility to the composition of finitely many instances of a theorem is captured by provability in EL₀ together with Markov’s principle, and that Weihrauch reducibility is captured by an affine subsystem of EL₀ plus Markov’s principle.</description><subject>Calculus</subject><subject>Mathematics</subject><subject>Theorems</subject><issn>0022-4812</issn><issn>1943-5886</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNo9kEtLw0AUhQdRsFZXroWAS0md92NnTKMZqCm0ieJqiJkJGKrRmXbhv3dKxc09i_txDnwAXCI4QxCJ2yFsZhgiPuPoCEyQoiRlUvJjMIEQ45RKhE_BWQgDhJApKifgblklL4UuV1mTl8mqmDe5vtcLXb8mWTVPdFU3utbLSq9rncf_c7FaF8lTVpdFPDpfn4OTvt0Ed_GXU9A8FHVepovlo86zRdoRqrYpVa0VkhHxRi20uGe2F23nBFeW9VAQpyS01nWs76hThLYttohQxIgV2PKeTMH1offLj987F7ZmGHf-M04aLKQgECnMI3VzoDo_huBdb778-0frfwyCZq_IREVmr8hwFOmrAz2E7ej_Ucx51KUI-QUipVzu</recordid><startdate>20171201</startdate><enddate>20171201</enddate><creator>KUYPER, RUTGER</creator><general>Association for Symbolic Logic, Inc</general><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>AABKS</scope><scope>ABSDQ</scope></search><sort><creationdate>20171201</creationdate><title>ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS</title><author>KUYPER, RUTGER</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c349t-49ad78537b4d0d2f5df7ace769d5f073e980ddec5fc4e934aa2d134153d72d6f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Calculus</topic><topic>Mathematics</topic><topic>Theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>KUYPER, RUTGER</creatorcontrib><collection>CrossRef</collection><collection>Philosophy Collection</collection><collection>Philosophy Database</collection><jtitle>The Journal of symbolic logic</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>KUYPER, RUTGER</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS</atitle><jtitle>The Journal of symbolic logic</jtitle><date>2017-12-01</date><risdate>2017</risdate><volume>82</volume><issue>4</issue><spage>1438</spage><epage>1458</epage><pages>1438-1458</pages><issn>0022-4812</issn><eissn>1943-5886</eissn><abstract>We show that there is a strong connection between Weihrauch reducibility on one hand, and provability in EL₀, the intuitionistic version of RCA₀, on the other hand. More precisely, we show that Weihrauch reducibility to the composition of finitely many instances of a theorem is captured by provability in EL₀ together with Markov’s principle, and that Weihrauch reducibility is captured by an affine subsystem of EL₀ plus Markov’s principle.</abstract><cop>Pasadena</cop><pub>Association for Symbolic Logic, Inc</pub><doi>10.1017/jsl.2016.61</doi><tpages>21</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0022-4812
ispartof The Journal of symbolic logic, 2017-12, Vol.82 (4), p.1438-1458
issn 0022-4812
1943-5886
language eng
recordid cdi_proquest_journals_2787301926
source JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Cambridge University Press Journals Complete
subjects Calculus
Mathematics
Theorems
title ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-19T08%3A22%3A37IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=ON%20WEIHRAUCH%20REDUCIBILITY%20AND%20INTUITIONISTIC%20REVERSE%20MATHEMATICS&rft.jtitle=The%20Journal%20of%20symbolic%20logic&rft.au=KUYPER,%20RUTGER&rft.date=2017-12-01&rft.volume=82&rft.issue=4&rft.spage=1438&rft.epage=1458&rft.pages=1438-1458&rft.issn=0022-4812&rft.eissn=1943-5886&rft_id=info:doi/10.1017/jsl.2016.61&rft_dat=%3Cjstor_proqu%3E26600293%3C/jstor_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2787301926&rft_id=info:pmid/&rft_jstor_id=26600293&rfr_iscdi=true