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unsolved

26.10.2023 · AE531026
Unsolved problems are problems for which we neither have a solution, nor know whether such solution can be found.
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solvable

26.10.2023 · AE531026
P is solvable if, at some point in time, a proof will be provided that solution to P can be found.

unsolvable

26.10.2023 · AE531026
P is unsolvable if, at some point in time, a proof will be provided that P does not have solution.
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fatal

26.10.2023 · AE531026
Problem P is "fatal" if no proof could ever be provided whether P is solvable or unsolvable. 

It is impossible to tell about problem if it is "fatal". That's why it is fatal ;)