Standard teaching is that God is omniscient. But what does the word mean? To most, it means "One who knows everything". To me, it means "One who knows everything that there is to know". Some things are simply not there for anyone to know.
Enter quantum mechanics, the most successful physical theory ever devised, predicting things correctly to seven decimal places. It says that Schrödinger's cat is both alive and dead, and only observation can bring one of these two possibilities into reality. Before observation, it is actually wrong to say "the cat is either alive or dead", because that statement leads to things different from what we observe in the laboratory. So even God does not "know" whether "the cat is alive or dead", because that knowledge is simply not there to be had.
So Rabbi Akiva's dictum, "Everything is foreseen and free will is given", means "Everything [that there is to foresee, namely the probabilities of occurrence of various outcomes,] is foreseen, and free will is given [because we can influence that outcome]".
As I see it, all the "infinity" attributes of God reflect the influence of Greek philosophy. They are not included in God's 13 attributes. The Rambam was careful to say, in his 10th principle of faith, that God knows what people are doing NOW, but adds nothing about their future:
The Tenth Foundation is that God, blessed be He, knows the actions of mankind and does not turn His eyes from them... "Great in counsel, and mighty in work; for your eyes are open upon all the ways of the sons of men; to give to every one according to his ways, and according to the fruit of his doings" (Jeremiah 32:19).
So, my question is: Where, in traditional sources ancient and modern, is the definition of "omniscience" discussed?