Computability in Europe 2006
Logical Approaches to Computational Barriers

Regular Talk:
Phase transitions for weakly increasing sequences

Speaker: Michiel De Smet
Author(s): Michiel De Smet and Andreas Weiermann
Slot: Array, 11:50-12:10, col. 1


Motivated by the classical Ramsey for pairs problem in reverse mathematics we investigate the recursion-theoretic complexity of certain assertions which are related to the Erdös-Szekeres theorem. We show that resulting density principles give rise to Ackermannian growth. We then parameterize these assertions with respect to a number-theoretic function f and investigate for which functions f Ackermannian growth is still preserved. We show that this is the case for f(i) = sqrt[d](i) but not for f(i) = log(i).

websites: Arnold Beckmann 2008-06-12