Yes! And God's power is bigger than the limitations we put on His power. Always.
But pointing out that God must operate within logic isn't "limiting" His power at all. It's just winnowing nonsense statements out of the picture.
For instance, the reason why the often asked question, "Can God create a rock so large that He can't lift it?" isn't a valid objection to omnipotence because it's not a logical possibility, and omnipotence is often defined as the capacity to actualize any logically possible state of affairs.
It's also not possible for God to be God and not-God at the same time and in the same respect, that would be absurd. Nor can God create a Euclidean square-circle. However an omnipotent being can change any physical laws as He sees fit, such as gravity, electromagnetism, and so on since doing so doesn't violate logic.
The "creating a rock so heavy even God can't lift it" bit fails because it's exactly the same thing as the non-question, "What happens if an irresistable force meets an immovable object?" Well, if an irresistable force exists then there can't be such a thing as an immovable object (otherwise the force is resistable by at least one thing: the immovable object). Likewise if an immovable object exists there can't be such a thing as an irresistable force (otherwise the object is movable to at least one thing: the irresistable force).
God can create either an immovable object or an irresistable force (in some ways God is an irresistable force) but not both at the same time by definition.
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