Logical Approaches to Computational Barriers

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 |