It has been a longstanding problem whether kaon condensation is realized
in high-density matter. We have investigated possible coexistence of kaon
condensates and hyperon-mixed matter as multi-strangeness system on the
basis of chiral symmetry for kaon(K)-baryon(B) and K-K interactions , combined
with the relativistic mean field theory for B-B interaction.
From the viewpoint that both kaons and hyperons should naturally appear in high
densities, it is shown that the three-body forces (TBR for repulsion, TBA for attraction)
for baryons should be introduced phenomenologically in order to obtain a stiff
equation of state (EOS) which is consistent with recent observations of massive
neutron stars.
We further discuss the effect of the isovector part of the TBA on the radius of
neutron stars and rapid neutrino emission mechanisms in kaon condensates
and their effects on thermal evolution of neutron stars.