Omniscience is the property of having complete maximal knowledge. It's integral to the 'perfect being' theology. God, believe most theists, is all-knowing.
If God is omniscient, that is He possesses a set of all truths, then this entails a powerset (a set of all subsets). The powerset of Godâs set of all truths would be greater in cardinality than the original set (Per Cantorâs theorem). Therefore, no being, as omniscient as that could possibly mean, can have complete knowledge of His knowledge. Therefore, itâs logically impossible for a being to be omniscient in the sense of possessing a set of all truths. If God knows (as a matter of fact) that Iâm going to do action A tomorrow afternoon, then action A canât fail to obtain. Action A either obtains, in which case I couldnât do otherwise. Or action A doesnât obtain, in which case God holds a false belief. Theists unanimously would consider the latter unacceptable. So letâs consider the following hypothetical. We know things about ourselves which God canât possibly know unless He becomes, somehow, identical to us. Moreover, God canât be omniscient because there could be something that He is not aware of the fact that He doesnât know it. He wonât be able to say there isnât because He wouldnât know it if there were any.