Some elementary closure properties of n-cylinders

(i) A set is a cylinder if and only if it is an ^-cylinder for each n > 1. (ii) The class of all (n+l)-cylinders is a proper subset of the class of all π-cylinders for each n > 1. (iii) For each n > 1, the class of all ^-cylinders contains a simple set and hence a nonsplinter. (iv) For each n > 1, the class of all ^-cylinders contains a nonsimple nonsplinter. (v) A set P is an ^-cylinder (n > 1) if and only if there is a recursive function g such that for all x,