On Lack of Effectiveness in Semi-algebraic Geometry

  • Riccardo Benedetti
Part of the Progress in Mathematics book series (PM, volume 94)


It is a fact and a motivation of this meeting, that many interesting constructions in semi-algebraic geometry can be effectively done, that is, roughly speaking, by means of algorithms with computably bounded complexity. It is also a fact that semi-algebraic objects have some effective finiteness properties. Hence the interest in finding reasonably ”fast” algorithms or “sharp” bounds. Neverthless, on the other side of the mainstream, one can be interested in essential lack of effectiveness or finiteness. We are going to see some examples and to discuss shortly some possible basic sources of such a lack.


Simplicial Complex Computable Function Topological Type Secant Approximation Whitney Stratification 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Riccardo Benedetti
    • 1
  1. 1.Dipartimento di MatematicaPisaItaly

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