"Har fel" is for when someone is wrong about something. "Han har fel" -> "He is wrong".
Same for "Har rätt". "Han har rätt" -> "He's right".
When something is wrong on it's own, it's "Är fel".
Shouldn't definitively be accepted as a translation of definitivt? It's a tad stronger claim than definitely, but still means about the same thing, if I'm not mistaken.
"His definition is definitely false." is marked as false. Why? Are "false" and "wrong" really that different?
False means that it's a lie, whereas wrong means that it's just not correct