Can a cat get Alzheimers?

Ok this is going to sound a bit silly, but is it possible for a cat to get Alzheimers? Or is there some sort of degenerative brain thing that a cat can get?

My cat is 16 and she's nuts! She has been a screamer since she was a baby, meows LOUD & pretty constantly. Lately though she will meow to get inside then less than a minute later will want to go back out & this will continue for ages, it's like she forgets where she wants to be. She also does it with food, finishes eating then less than five minutes later she cries for more, but if you give her more she won't eat it because she's already full.

Is it possible there is something wrong, or is it just because she's getting older?

They can go a bit loopy. Can you take her to the vets for a checkup?

Cats can get dementia. My parents cat has dementia.

Really? Can they do anything or is it just something you cope with? How did they find out?