Computability in Europe 2008
Logic and Theory of Algorithms

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Regular Talk:
Phase transitions for weakly increasing sequences

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

Abstract

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).


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