[Cross-posted at Prosblogion] Open theists distinguish between two different varieties of their view. There are actually a number of ways to divide up open theism into varieties, but one particular division that open theists make among themselves is between the following two positions:
1. There is no such thing as a future to be known, and that's why God doesn't know the future exhaustively. It's not a limitation on God that he doesn't know everything that will happen. There's nothing to be known, so God can't know it. So God is omniscient in knowing all the facts about the future. There just aren't very much such facts yet.
2. God could know the future, but it would prevent our freedom, so God chooses to limit his knowledge, knowing that knowledge about what we would choose to do would make us unfree. God doesn't know all he could know metaphysically, but he does know all he could know given his choice not to know future free choices.
I'm not really sure these are distinct views. It sounds as if one view has God unable to know the future, and the other has him able to know it but choosing not to. But think about what would make him unable to know the future in the first case and unwilling to know it in the second. If he's unable to know the future because there's no future to be known, we're working with a picture of a world that's not deterministic. When people make free choices, they can do otherwise, and the idea is that open choices like that require an open future, which requires there being no fact about what you will do until you do it. But on view 1, it seems God could arrange for me to choose a certain thing. I just wouldn't be free if God did that. So God chooses not to know what I'll do in order to ensure that I have the chance to make free choices. But isn't that view 2?
Now think about the second view. What would happen if God chose to know what I'd do ahead of time? On view 2, I wouldn't be free if God chose such a thing. So God voluntarily chooses not to make me unfree, and he chooses to let the future be open with respect to my choice, which means he can't know my future choice, and we're really dealing with view 1.
So I'm not really sure these views are different views after all. In both views, God could know what I will do, and it would require me not being free. View 1 expresses this by assuming God won't ensure that I do any particular thing and then says God can't know my future choice. View 2 expresses it by making it explicit that God has chosen not to know and acknowledging that God could have known but it would mean I'm not free. But I'm not sure we're dealing with a different picture of what's going on, just a different way of describing it.