Can't "Han troede ikke på kvinden" also mean "He didn't think of the woman", since, as far as I recall, 'at tænke på' can also mean 'to think of'? Or did I just misremember?
If it is talking about a thought of the woman, it would be "Han tænkte ikke på kvinden".
The på after troede turns the meaning from "think" to "believe" in this case (as "at tro" on its can't have a direct object)
Oh, okay, thanks!
How do you say 'believe in' as in 'he didn't believe in ghosts'?