  Oscillations and propagating waves are commonly seen in high-resolution
observations of filament threads, i.e., the fine-structures of solar
filaments/prominences. Since the temperature of prominences is typically of the
order of 10^4 K, the prominence plasma is only partially ionized. In this
paper, we study the effect of neutrals on the wave propagation in a filament
thread modeled as a partially ionized homogeneous magnetic flux tube embedded
in an homogeneous and fully ionized coronal plasma. Ohmic and ambipolar
magnetic diffusion are considered in the basic resistive MHD equations. We
numerically compute the eigenfrequencies of kink, slow, and Alfven linear MHD
modes, and obtain analytical approximations in some cases. We find that the
existence of propagating modes is constrained by the presence of critical
values of the longitudinal wavenumber. In particular, the lower and upper
frequency cut-offs of kink and Alfven waves owe their existence to magnetic
diffusion parallel and perpendicular to magnetic field lines, respectively. The
slow mode only has a lower frequency cut-off, which is caused by perpendicular
magnetic diffusion and is significantly affected by the ionization degree. In
addition, ion-neutral collisions is the most efficient damping mechanism for
short wavelengths while ohmic diffusion dominates in the long-wavelength
regime.
