# On Lack of Effectiveness in Semi-algebraic Geometry

Chapter

## Abstract

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.

## Keywords

Simplicial Complex Computable Function Topological Type Secant Approximation Whitney Stratification
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© Springer Science+Business Media New York 1991