Are there set-theoretical problems with modal metaphysics?

I'm trying to learn about modal logic and the metaphysics of modality, and there's something that has been bugging me about what I've read so far: are there set-theoretical issues with supposing we can refer to every possible world? I'm not worried about models with finitely many worlds, but some of the modal metaphysics I've read defines the set of possible worlds (i.e, W) as something like "a set that contains all and only the maximally consistent sets of propositions". This makes me nervous for two reasons:

Reason 1: If w is a possible world then, for every subset s of w, the proposition "s is a subset of w" is true (and therefore should be an element of w). This makes it seem like w contains an element for every subset of itself. But if that were true, then the power set of w would have a cardinality equal to or less than w, which is impossible.

Reason 2: It seems like it would be possible for the world to consist of a point particle in R^3.Because the point particle exists in a real number space, there are an uncountable number of places such a particle could be. Does this imply that the set of possible worlds is uncountable? And, if it is uncountable, is that a problem?

Any clarification of these issues would be greatly appreciated. Thanks.

• Note that something like "the set of all maximally consistent sets of propositions" is actually quite small, from a set-theoretic standpoint anyways, as long as "proposition" means something reasonable: e.g. if by "proposition" we mean (say) "first-order sentence in the language of set theory," then there are only countably many of those and so our desired set is ... exactly as big as the set of real numbers. This is only problematic if we're skeptical of uncountable sets in the first place. (Note that your first issue arises from not being careful about what "proposition" means.) Sep 21 '20 at 3:45
• If w is a set of propositions then "s is a subset of w" is not in w. The propositions are meant to be about world's objects and relations, not about other propositions or their sets, they are not second order. There is no problem not only if W is uncountable, but if it is not even a set but a proper class. A simple example is the class of all models of a formal theory, which may contain models of any cardinality, and hence not be a set. Nothing in modal talk requires dealing with all possible worlds as a collection, so it need not be a set (but usually is). Sep 21 '20 at 7:01