10 citations · 22 across the 22 of their papers we have counts for
24 papers
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…
The Ouroboros Goodstein Principle
David Fernández-Duque, Milan Morreel, Andreas Weiermann
In arXiv:2508.14768, a variant of Goodstein's original process was recently introduced which, given a set of bases, writes each in -norm…
The fractal Goodstein principle
David Fernández-Duque, Andreas Weiermann
The original Goodstein process is based on writing numbers in hereditary -exponential normal form: that is, each number is written in some base as , with…
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 -logic is induction on dilators. In particular, Girard used this principle to construct his famous functor . He cla…
Optimal Image Transport on Sparse Dictionaries
Junqing Huang, Haihui Wang, Andreas Weiermann +1
In this paper, we derive a novel optimal image transport algorithm over sparse dictionaries by taking advantage of Sparse Representation (SR) and Optimal Transport (OT). Concisely,…
Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal
David Fernández-Duque, Andreas Weiermann
We prove that Buchholz's system of fundamental sequences for the function enjoys various regularity conditions, including the Bachmann property. We partially extend the…