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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De Smet, M., Weiermann, A. (2008). Phase Transitions for Weakly Increasing Sequences. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_20
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DOI: https://doi.org/10.1007/978-3-540-69407-6_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69405-2
Online ISBN: 978-3-540-69407-6
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