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$%N. Dutertre, About the Euler-Poincaré characteristic of semi-algebraic sets defined with two inequalities, Rev. Mat. Complut. 14 (2001), no. 1, 45–82.%$

We express the Euler-Poincaré characteristic of a semi-algebraic set, which is the intersection of a non-singular complete intersection with two polynomial inequalities, in terms of the signatures of appropriate bilinear symmetric forms.

2000 Mathematics Subject Classification: 14P10, 14P25.