FOM: A question about model theory

[John Goodrick]

A quick question for the model theorists:

1. Is any totally disconnected compact Hausdorff space homeomorphic to a
Stone space?  If not, do you have a counterexample?

2. Is any first-countable, totally disconnected, compact Hausdorff space
homeomorphic to the Stone space of a countable set in a model with a
countable language?  Counterexample?

-John