Classifying the phase transition threshold for Ackermannian functions

Eran Omri; Andreas Weiermann

doi:10.1016/j.apal.2007.02.004

Classifying the phase transition threshold for Ackermannian functions

Eran Omri, Andreas Weiermann

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

It is well known that the Ackermann function can be defined via diagonalization from an iteration hierarchy (of Grzegorczyk type) which is built on a start function like the successor function. In this paper we study for a given start function g iteration hierarchies with a sub-linear modulus h of iteration. In terms of g and h we classify the phase transition for the resulting diagonal function from being primitive recursive to being Ackermannian.

Original language	English
Pages (from-to)	156-162
Number of pages	7
Journal	Annals of Pure and Applied Logic
Volume	158
Issue number	3
DOIs	https://doi.org/10.1016/j.apal.2007.02.004
State	Published - Apr 2009
Externally published	Yes

Keywords

Ackermann function
Fast growing hierarchy
Phase transition
Threshold

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10.1016/j.apal.2007.02.004

Cite this

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KW - Ackermann function

KW - Fast growing hierarchy

KW - Phase transition

KW - Threshold

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Classifying the phase transition threshold for Ackermannian functions

Abstract

Keywords

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