A. Weiermann

activity

20242026

collaborators

5 papers

math.LO2026

A Walk with Goodstein and Ackermann

David Fernández-Duque, Andreas Weiermann

Goodstein's theorem states that a certain sequences based on exponential notation for the natural numbers are always finite. The result is independent of Peano arithmetic and is a…

math.LO2026

The Ouroboros Goodstein Principle

David FernÃ¡ndez-Duque, Milan Morreel, Andreas Weiermann

In arXiv:2508.14768, a variant of Goodstein's original process was recently introduced which, given a set $B \subseteq N$ of bases, writes each $n \in N$ in $B$ -norm…

math.LO2025

The fractal Goodstein principle

David FernÃ¡ndez-Duque, Andreas Weiermann

The original Goodstein process is based on writing numbers in hereditary $b$ -exponential normal form: that is, each number $n$ is written in some base $b \geq 2$ as $n = b^{e} a + r$ , with…

math.LO2025

Maximum linearizations of lower sets in $N^{m}$ with application to monomial ideals

Harry Altman, Andreas Weiermann

We compute the type (maximum linearization) of the well partial order of bounded lower sets in $N^{m}$ , ordered under inclusion, and find it is $I ¨ ^{I ¨ ^{m - 1}}$ . Moreover we…

math.LO2024

Induction on Dilators and Bachmann-Howard Fixed Points

Juan P. Aguilera, Anton Freund, Andreas Weiermann

One of the most important principles of J.-Y. Girard's $I^_{2}^{1}$ -logic is induction on dilators. In particular, Girard used this principle to construct his famous functor $I^$ . He c…