  We discuss some properties of a model Hamiltonian for a system of three
bosons interacting via zero-range forces in three dimensions. In order to avoid
the well known instability phenomenon, we consider the so-called Minlos-Faddeev
regularization of such Hamiltonian, heuristically corresponding to the
introduction of a three-body repulsion. We review the main concerning results
recently obtained. In particular, starting from a suitable quadratic form $Q$,
the self-adjoint and bounded from below Hamiltonian $\mathcal H$ can be
constructed provided that the strength $\gamma$ of the three-body force is
larger than a threshold parameter $\gamma_c$. Moreover, we give an alternative
and much simpler proof of the above result whenever $\gamma > \gamma'_c$, with
$\gamma'_c$ strictly larger than $\gamma_c$. Finally, we show that the
threshold value $\gamma_c$ is optimal, in the sense that the quadratic form $Q$
is unbounded from below if $\gamma<\gamma_c$.
