论文信息 - Primitive recursive bounds for van der Waerden numbers

Primitive recursive bounds for van der Waerden numbers

a = 1, a+ = 2U(n,c '), i > O. Then U(n + ?, c) = ac . In order to get some idea of the rate of growth of U(n, c) (and of the functions which will be introduced later in this paper), we shall define the classes of the Grzegorczyk hierarchy. For each n E N, define a function En by Eo(x, y) = x + y, E1 (x) = x2 + 2, En+2(0) = 2, En,2 (x + 1) = En+ I (En+2 () Then, for example, 2 2x< E2 (X) < 3 3 *~~~~ v Presented at a meeting of the British Mathematics Colloquium; received by the editors February 10, 1988. 1980 Mathematics Subject Classification (1985 Revision). Primary 05A99; Secondary 1 5A03.

Saharon Shelah | S. Shelah

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