We give upper bounds for a positional game — in the sense of Beck — based on the Paris-Harrington principle for bi-colorings of graphs and uniform hypergraphs of arbitrary dimension. The bounds show a striking difference with respect to the bounds of the combinatorial principle itself. Our results confirm a phenomenon already observed by Beck and others: the upper bounds for the game version of...

Sir,—The use of distraction and compression rods in the treatment of scoliosis was originally described by Harrington (1962). One of the complications of this operation is paraplegia, with a reported frequency of 0.1% (Harrington, 1971). To prevent this complication, patients are wakened during operation to check the voluntary motor power of the limbs. A variety of wake-up techniques has been d...

Harrington and Soare introduced the notion of an n-tardy set. They showed that there is a nonempty E property Q(A) such that if Q(A) then A is 2tardy. Since they also showed no 2-tardy set is complete, Harrington and Soare showed that there exists an orbit of computably enumerable sets such that every set in that orbit is incomplete. Our study of n-tardy sets takes off from where Harrington and...