What's the noun for appealability? Here's the word you're looking for.
appeal
(law)
An application for the removal of a cause or suit from an inferior to a superior judge or court for re-examination or review.
The mode of proceeding by which such removal is effected.
The right of appeal.
An accusation; a process which formerly might be instituted by one private person against another for some heinous crime demanding punishment for the particular injury suffered, rather than for the offense against the public.
An accusation of a felon at common law by one of his accomplices, which accomplice was then called an approver.
“This exception relates to the appealability of the case. Often the very first issue before the appellate court is whether the court should hear the appeal.”