  GW170817 is the very first observation of gravitational waves originating
from the coalescence of two compact objects in the mass range of neutron stars,
accompanied by electromagnetic counterparts, and offers an opportunity to
directly probe the internal structure of neutron stars. We perform Bayesian
model selection on a wide range of theoretical predictions for the neutron star
equation of state. For the binary neutron star hypothesis, we find that we
cannot rule out the majority of theoretical models considered. In addition, the
gravitational-wave data alone does not rule out the possibility that one or
both objects were low-mass black holes. We discuss the possible outcomes in the
case of a binary neutron star merger, finding that all scenarios from prompt
collapse to long-lived or even stable remnants are possible. For long-lived
remnants, we place an upper limit of 1.9 kHz on the rotation rate. If a black
hole was formed any time after merger and the coalescing stars were slowly
rotating, then the maximum baryonic mass of non-rotating neutron stars is at
most 3.05 $M_\odot$, and three equations of state considered here can be ruled
out. We obtain a tighter limit of 2.67 $M_\odot$ for the case that the merger
results in a hypermassive neutron star.
