  We present a brief historical introduction to the topic of Bell's theorem.
Next we present the surprising features of the three particle
Greenberger-Horne-Zeilinger (GHZ) states. Finally we shall present a method of
analysis of the GHZ correlations, which is based on a numerical approach, which
is effectively equivalent to the full set of Bell inequalities for correlation
functions for the given problem. The aim of our numerical approach is to answer
the following question. Do additional possible local settings lead for the GHZ
states to more pronounced violation of local realism (measured by the
resistance of the quantum nature of the correlations with respect ``white''
noise admixtures)?
