  A set of all symmetric Banach function spaces defined on [0,1] is equipped
with the partial order by the relation of continuous inclusion. Properties of
symmetric spaces, which do not depend of their position in the ordered
structure, are studied. With the help of the J. Peetre's interpolation scheme
it is shown that for any pair of symmetric spaces E, F such that F is
absolutely continuously included in E there exists an intermediate (so called,
Peetre's) space K(E,F;W), where W is a space with an unconditional basis, that
is reflexive or, respectively, weakly sequentially complete provided W also is
reflexive or, respectively, weakly sequentially complete.
