There’s increasing talk these days about a “limited God,” but I often find the general statement unhelpful. So, let’s see if we can get some clarity on the matter by distinguishing between a God that is limited in a way that doesn’t impugn His omnipotence (or really, His God-ness) and one that does.
An immediate difficulty, of course, concerns how one understands omnipotence, so let’s briefly address that. I’ve suggested before—in line with the scholastic tradition, I believe—that we shouldn’t think about omnipotence as the ability to “do anything” in the broadest sense, but more specifically as the ability to produce. That is, God can bring about any possible contingent state of affairs.
To be even more precise, I think we should understand omnipotence as God having a perfectly efficacious will, such that whether any possible contingent state of affairs occurs is essentially equivalent to God willing it. (More formally: Some being, S, is omnipotent iff for every logically contingent state of affairs, p, whether p or not-p is the case is logically equivalent to the effective choice of S that p or not-p.)