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...

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Veröffentlicht in:	Theoretical computer science 2004-12, Vol.328 (3), p.355-361
1. Verfasser:	Foy, John
Format:	Artikel
Sprache:	eng
Schlagworte:	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
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Zusammenfassung:	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.
ISSN:	0304-3975 1879-2294
DOI:	10.1016/j.tcs.2004.05.001