increase the $\Lambda$ chemical potential further in comparison with the NLO13 result plotted in fig.\[fig:chempot\], so as to widen the gap between $\mu_\Lambda$ and $\mu_n$ even more.

A further comment concerns $\Sigma$ hyperons in neutron star matter. At high density it is in principle possible to consider the condition $$\mu_{\Sigma^-} = \mu_n+\mu_e = 2\mu_n -\mu_p$$ for the occurrence of $\Sigma^-$ replacing an electron together with a neutron. However, this turns out not to be an option because the $\Sigma^-$ potential in neutron matter is strongly repulsive [@Petschauer2016b], so that $\mu_{\Sigma^-}$ remains separated by at least 50 MeV from $\mu_n + \mu_e$ at all relevant densities.

Summary and outlook {#sec:sum}
===================

Investigations of the properties of hyperons in nuclear and neutron matter have been extended to high baryon densities with the quest of exploring the possible occurrence of hyperons in neutron stars. Previous calculations based entirely on two-body hyperon-nucleon interactions suggested an onset for hyperons already at relatively low densities (between two and three times $\rho_0$). As a consequence the resulting equation-of-state is significantly softened and cannot support two-solar-mass neutron stars. The present work addresses the question whether hyperon-nucleon three-body forces (3BF) can provide the necessary repulsion to stop $\Lambda$ hyperons 