A dynamical system which must be stable whose stability cannot be proved
Building on a result of Blondel, we show that there exists a piecewise affine dynamical system whose stability (local asymptotic stability, global asymptotic stability and global convergence) is equivalent to the correctness of ZF set theory—a property which must be assumed to hold but which cannot...
Gespeichert in:
| Veröffentlicht in: | Theoretical computer science 2004-12, Vol.328 (3), p.355-361 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 361 |
|---|---|
| container_issue | 3 |
| container_start_page | 355 |
| container_title | Theoretical computer science |
| container_volume | 328 |
| creator | Foy, John |
| description | Building on a result of Blondel, we show that there exists a piecewise affine dynamical system whose stability (local asymptotic stability, global asymptotic stability and global convergence) is equivalent to the correctness of ZF set theory—a property which must be assumed to hold but which cannot be proved within ZF. |
| doi_str_mv | 10.1016/j.tcs.2004.05.001 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_28170146</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0304397504003639</els_id><sourcerecordid>28170146</sourcerecordid><originalsourceid>FETCH-LOGICAL-c399t-43b2e037b3d259b775c42119b25c899570088bf47a61fa2fb70ee9f4820500153</originalsourceid><addsrcrecordid>eNp9kE1PwzAMhiMEEuPjB3DrBW4tTpo0jThNCBjSJC5wjtLU1TL1Y9Td0P49GUPihi-WrcfvK7-M3XDIOPDifp1NnjIBIDNQGQA_YTNeapMKYeQpm0EOMs2NVufsgmgNsZQuZmwxT-p977rgXZvQnibskq9V8Kuk29KUVJjQ5KoW43Kg4xDaMO0T7_p--AE247DD-oqdNa4lvP7tl-zj-en9cZEu315eH-fL1OfGTKnMK4GQ6yqvhTKV1spLwbmphPKlMUoDlGXVSO0K3jjRVBoQTSNLASp-pfJLdnfUjbafW6TJdoE8tq3rcdiSFSXXwGURQX4E_TgQjdjYzRg6N-4tB3vIzK5tzMweMrOgbFSPN7e_4o5iIM3oeh_o77AQxggtI_dw5DB-ugs4WvIBe491GNFPth7CPy7ftTqAFw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>28170146</pqid></control><display><type>article</type><title>A dynamical system which must be stable whose stability cannot be proved</title><source>Elsevier ScienceDirect Journals Complete</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>Foy, John</creator><creatorcontrib>Foy, John</creatorcontrib><description>Building on a result of Blondel, we show that there exists a piecewise affine dynamical system whose stability (local asymptotic stability, global asymptotic stability and global convergence) is equivalent to the correctness of ZF set theory—a property which must be assumed to hold but which cannot be proved within ZF.</description><identifier>ISSN: 0304-3975</identifier><identifier>EISSN: 1879-2294</identifier><identifier>DOI: 10.1016/j.tcs.2004.05.001</identifier><identifier>CODEN: TCSCDI</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Correctness ; Dynamical systems ; Exact sciences and technology ; Global analysis, analysis on manifolds ; Hybrid systems ; Logic and foundations ; Mathematical logic, foundations, set theory ; Mathematics ; Piecewise affine systems ; Sciences and techniques of general use ; Set theory ; Stability ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Theoretical computer science, 2004-12, Vol.328 (3), p.355-361</ispartof><rights>2004 Elsevier B.V.</rights><rights>2005 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c399t-43b2e037b3d259b775c42119b25c899570088bf47a61fa2fb70ee9f4820500153</citedby><cites>FETCH-LOGICAL-c399t-43b2e037b3d259b775c42119b25c899570088bf47a61fa2fb70ee9f4820500153</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.tcs.2004.05.001$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16299274$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Foy, John</creatorcontrib><title>A dynamical system which must be stable whose stability cannot be proved</title><title>Theoretical computer science</title><description>Building on a result of Blondel, we show that there exists a piecewise affine dynamical system whose stability (local asymptotic stability, global asymptotic stability and global convergence) is equivalent to the correctness of ZF set theory—a property which must be assumed to hold but which cannot be proved within ZF.</description><subject>Correctness</subject><subject>Dynamical systems</subject><subject>Exact sciences and technology</subject><subject>Global analysis, analysis on manifolds</subject><subject>Hybrid systems</subject><subject>Logic and foundations</subject><subject>Mathematical logic, foundations, set theory</subject><subject>Mathematics</subject><subject>Piecewise affine systems</subject><subject>Sciences and techniques of general use</subject><subject>Set theory</subject><subject>Stability</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><issn>0304-3975</issn><issn>1879-2294</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><recordid>eNp9kE1PwzAMhiMEEuPjB3DrBW4tTpo0jThNCBjSJC5wjtLU1TL1Y9Td0P49GUPihi-WrcfvK7-M3XDIOPDifp1NnjIBIDNQGQA_YTNeapMKYeQpm0EOMs2NVufsgmgNsZQuZmwxT-p977rgXZvQnibskq9V8Kuk29KUVJjQ5KoW43Kg4xDaMO0T7_p--AE247DD-oqdNa4lvP7tl-zj-en9cZEu315eH-fL1OfGTKnMK4GQ6yqvhTKV1spLwbmphPKlMUoDlGXVSO0K3jjRVBoQTSNLASp-pfJLdnfUjbafW6TJdoE8tq3rcdiSFSXXwGURQX4E_TgQjdjYzRg6N-4tB3vIzK5tzMweMrOgbFSPN7e_4o5iIM3oeh_o77AQxggtI_dw5DB-ugs4WvIBe491GNFPth7CPy7ftTqAFw</recordid><startdate>20041203</startdate><enddate>20041203</enddate><creator>Foy, John</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20041203</creationdate><title>A dynamical system which must be stable whose stability cannot be proved</title><author>Foy, John</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c399t-43b2e037b3d259b775c42119b25c899570088bf47a61fa2fb70ee9f4820500153</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Correctness</topic><topic>Dynamical systems</topic><topic>Exact sciences and technology</topic><topic>Global analysis, analysis on manifolds</topic><topic>Hybrid systems</topic><topic>Logic and foundations</topic><topic>Mathematical logic, foundations, set theory</topic><topic>Mathematics</topic><topic>Piecewise affine systems</topic><topic>Sciences and techniques of general use</topic><topic>Set theory</topic><topic>Stability</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Foy, John</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Theoretical computer science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Foy, John</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A dynamical system which must be stable whose stability cannot be proved</atitle><jtitle>Theoretical computer science</jtitle><date>2004-12-03</date><risdate>2004</risdate><volume>328</volume><issue>3</issue><spage>355</spage><epage>361</epage><pages>355-361</pages><issn>0304-3975</issn><eissn>1879-2294</eissn><coden>TCSCDI</coden><abstract>Building on a result of Blondel, we show that there exists a piecewise affine dynamical system whose stability (local asymptotic stability, global asymptotic stability and global convergence) is equivalent to the correctness of ZF set theory—a property which must be assumed to hold but which cannot be proved within ZF.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.tcs.2004.05.001</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0304-3975 |
| ispartof | Theoretical computer science, 2004-12, Vol.328 (3), p.355-361 |
| issn | 0304-3975 1879-2294 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_28170146 |
| source | Elsevier ScienceDirect Journals Complete; EZB-FREE-00999 freely available EZB journals |
| subjects | Correctness Dynamical systems Exact sciences and technology Global analysis, analysis on manifolds Hybrid systems Logic and foundations Mathematical logic, foundations, set theory Mathematics Piecewise affine systems Sciences and techniques of general use Set theory Stability Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | A dynamical system which must be stable whose stability cannot be proved |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T09%3A00%3A17IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20dynamical%20system%20which%20must%20be%20stable%20whose%20stability%20cannot%20be%20proved&rft.jtitle=Theoretical%20computer%20science&rft.au=Foy,%20John&rft.date=2004-12-03&rft.volume=328&rft.issue=3&rft.spage=355&rft.epage=361&rft.pages=355-361&rft.issn=0304-3975&rft.eissn=1879-2294&rft.coden=TCSCDI&rft_id=info:doi/10.1016/j.tcs.2004.05.001&rft_dat=%3Cproquest_cross%3E28170146%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=28170146&rft_id=info:pmid/&rft_els_id=S0304397504003639&rfr_iscdi=true |