  We extend two kinds of causal models, structural equation models and
simulation models, to infinite variable spaces. This enables a semantics for
conditionals founded on a calculus of intervention, and axiomatization of
causal reasoning for rich, expressive generative models -- including those in
which a causal representation exists only implicitly -- in an open-universe
setting. Further, we show that under suitable restrictions the two kinds of
models are equivalent, perhaps surprisingly as their axiomatizations differ
substantially in the general case. We give a series of complete axiomatizations
in which the open-universe nature of the setting is seen to be essential.
