I would say it is what they call a no FG Kennedy half. I remember when these were discovered in 1984 and I do think that either Coin World and or Coin Prices or one of those magazine/price guides did an article on it. I think it was the 1984 P anyway that made it a celebrity of sorts in the Kennedy corner. They were selling for anywhere from $3.00 to $10.00 if I recall correctly. I think there are other dates known but this one was pretty famous. Maybe somebody will correct me if I'm wrong. It could have been an 1982 P too, maybe that was the year I am thinking of. Anyways, I think they are interesting but I don't think they have that sensational collectability they had as when they came out and as far as paying prices go, I think they are fairly inexpensive. It is a place where grease and debris is likely to get stuck on the dies. Some show none of the FG initials, while others so called no FG halves that I see for sale will still have a hint of it showing. I don't see the FG on your pictures. If you like it, congrats on finding one.
As a bit of a follow up, to clarify... The "true" No-FG was due to die use and abrasion, not grease or debris. Most of the "light FG" or "almost no FG" coins are the latter. It's worth noting that a "true" no FG has some other identifiers as well...most notably in the case of this particular coin, they have some VERY mushy tail feathers, which are apparent in the first image, at least as best as we can tell. There's also some identifiers in the stars, which are frequently very weak as well, and if I recall there's a die crack or scratch somewhere on the obverse as well, but i forget where now. In any event, judging best I can from those photos, the tail feathers certainly look "correct" to me.
When you turn the coin sideways and back again, can you see a "ghost image” or any trace of the “FG”? If the answer is yes, then it is not.
It looks like the pictures were taken through a loupe - that's why the edges don't show in the photos.
