'advanced degree' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for phd that I've seen before include "Highest university degree" , "Letters denoting holder of university doctorate" , "Initially a top university degree" , "In brief, top university qualification" .)
(Other definitions for nth that I've seen before include "Umpteenth" , "To the -- degree" .)