Olive oil fights Alzheimer's too? I heard (anecdotal) evidence for COCONUT oil, but never olive.

Another hit on your list: turmeric. I read in a nutrition book that its antioxidant properties are so strong that it may explain why Indians have to little incidence of brain problems (dementia, etc.). And if you combine it with black pepper, you have the most potent antioxidant possible! And cheap at that, at least in the US