### S. Shelah, L. Soukup:

##
The existence of large ` omega_1`-homogeneous
but not `omega`-homogeneous
permutation groups is consistent with ZFC + GCH

Denote by `Perm(lambda)` the group
of all permutations of a cardinal `lambda`.
A subgroup `G` of `Perm(lambda)`
is called `kappa`-*homogeneous* iff
for all `X,Y\in [lambda]^kappa`
there is a `g\in G` with `g''X=Y`. We show that if either
(i) `diamond^+` holds
and we add `omega_1` Cohen reals to the ground model,
or (ii) we add `2^{omega_1}` Cohen reals to the ground model,
then in the generic extension
for each `lambda>=omega_2` there is an
`omega_1`-homogeneous subgroup
of `Perm(lambda)` which is
not `omega`-homogeneous.

### Downloading the paper

** appeared in ** * J. London. Math. Soc. * 48 (1993), no 2 193--203.