Speaker
Oriola Gjetaj
Ghent University
Talks at this conference:
Friday, 14:50, J335 
A Goodstein independence result for $ID_2$ 
Authors: David FernandezDuque, Oriola Gjetaj and Andreas Weiermann The Goodstein principle is a natural numbertheoretic theorem. The original process works by writing natural numbers into nested exponential kbase normal form, then successively raising the base to k + 1 and subtracting 1 from the result. Such sequences always reach zero, but this fact is unprovable in Peano arithmetic. Drawing from previous results in the literature, we consider canonical representations with respect to the FastGrowing Extended Grzegorczyk hierarchy \(\{F_{a}\}_{a<\psi_0(\varepsilon_{\Omega+1})}\). Normal forms are written as basek representations and the component \(a\) is written as base\(\psi_0(\cdot)\) collapsing function up to BachmannHoward ordinal. We use an ordinal assignment to show that this sequence terminates and yields an independence result from the theory of \(ID_2\). This is part of joint work with A. Weiermann and D. Fern'andezDuque on exploring normal form notations for the Goodstein principle. Bibliography
