G. Wilken

activity

20122026

most citedPure patterns of order 2

6 citations · 13 across the 6 of their papers we have counts for

collaborators

7 papers

math.LO2026

Uniform generalization of Goodstein's theorem and Cichon's independence proof

Gunnar Wilken

We uniformly generalize Goodstein's theorem (Goodstein 1944) and Cichon's independence proof (Cichon 1983) via the concept of maximality quotients.

math.LO2025

Generalizing Goodstein's theorem and Cichon's independence proof

Gunnar Wilken

We generalize Goodstein's theorem (Goodstein 1944) and Cichon's independence proof (Cichon 1983) to $Π_{1}^{1} - CA_{0}$ using results from (Wilken 2026). The method is generaliza…

math.LO2024

Fundamental sequences based on localization

Gunnar Wilken

Building on Buchholz' assignment for ordinals below Bachmann-Howard ordinal, see Buchholz 2003, we introduce systems of fundamental sequences for two kinds of relativized $\varthet…

math.LO2017★ 2 cited

Pure $Σ_{2}$ -Elementarity beyond the Core

Gunnar Wilken

We display the entire structure $R_{2}$ coding $Σ_{1}$ - and $Σ_{2}$ -elementarity on the ordinals. This will enable the analysis of pure $Σ_{3}$ -elementary substructures.

math.LO2016★ 5 cited

Tracking chains revisited

Gunnar Wilken

The structure $C_{2} := (1^{\infty}, \leq, \leq_{1}, \leq_{2})$ , introduced and first analyzed in Carlson and Wilken 2012 (APAL), is shown to be elementary recursive. Here, $1^{\infty}$ denot…

math.LO2016★ 6 cited

Pure patterns of order 2

Gunnar Wilken

We provide mutual elementary recursive order isomorphisms between classical ordinal notations, based on Skolem hulling, and notations from pure elementary patterns of resemblance o…

Uniform generalization of Goodstein's theorem and Cichon's independence proof

Generalizing Goodstein's theorem and Cichon's independence proof

Fundamental sequences based on localization

Pure Σ2​-Elementarity beyond the Core

Tracking chains revisited

Pure patterns of order 2

Pure $Σ_{2}$ -Elementarity beyond the Core