"hydra game" . . . . "Goodstein's theorem" . . . . "Goodstein's theorem#Sequence length as a function of the starting value" . . . . . "hydra theorem" . . . . . "Kirby\u2013Paris theorem" . . "Goodstein's theorem" . . . . . . "Hereditary base-n notation" . . "Goodstein function" . . . . "Goodstein sequences" .