I'm community wikiing this, since although I don't want it to be a discussion thread, I don't think that there is really a right answer to this.

From what I've seen, model theorists and logicians are mostly opposed to GCH, while on the other end of the spectrum, some functional analysis depends on GCH, so it is much better tolerated among functional analysts. In fact, I considered myself very much +GCH for a while, but Joel and Francois noted some interesting stuff about forcing axioms, (the more powerful ones directly contradict CH).

What is the general opinion on GCH in the mathematical community (replace GCH with CH where necessary)? Does it happen to be that CH/GCH doesn't often come up in algebra?

Please don't post just post "I agree with +-CH". I'd like your assessment of the mathematical community's opinion. Maybe your experiences with mathematicians you know, etc. Even your own experiences or opinion can work. I am just not interested in having 30 or 40 one line answers. Essentially, I'm not looking for a poll.

Edit: GCH=Generalized Continuum Hypothesis CH= Continuum Hypothesis

CH says that $\aleph_1=\mathfrak{c}$. That is, the successor cardinal of $\aleph_0$ is the continuum. The generalized form (GCH) says that for any infinite cardinal $\kappa$, we have $\kappa^+=2^\kappa$, that is, there are no cardinals strictly between $\kappa$ and $2^\kappa$.

Edit 2 (Harry): Changed the wording about FA. If it still isn't true, and you can improve it, feel free to edit the post yourself and change it.

willdepend on it unless one restricts to separable spaces (or separable preduals) – Yemon Choi Feb 6 '10 at 2:05