  This paper studies homogenization of symmetric non-local Dirichlet forms with
$\alpha$-stable-like jumping kernels in one-parameter stationary ergodic
environment. Under suitable conditions, we establish homogenization results and
identify the limiting effective Dirichlet forms explicitly. The coefficients of
the jumping kernels of Dirichlet forms and symmetrizing measures are allowed to
be degenerate and unbounded; and the coefficients in the effective Dirichlet
forms can be degenerate.
