5 papers
Monadic second order limit laws for natural well orderings
Andreas Weiermann
By combining classical results of Büchi, some elementary Tauberian theorems and some basic tools from logic and combinatorics we show that every ordinal with $\varepsilon_0\geq…
Giant and illusionary giant Goodstein principles
Andreas Weiermann
We analyze several natural Goodstein principles which themselves are defined with respect to the Ackermann function and the extended Ackermann function. These Ackermann functions a…
Minimal bad sequences are necessary for a uniform Kruskal theorem
Anton Freund, Michael Rathjen, Andreas Weiermann
The minimal bad sequence argument due to Nash-Williams is a powerful tool in combinatorics with important implications for theoretical computer science. In particular, it yields a…
Predicatively unprovable termination of the Ackermannian Goodstein process
Toshiyasu Arai, David Fernández-Duque, Stanley Wainer +1
The classical Goodstein process gives rise to long but finite sequences of natural numbers whose termination is not provable in Peano arithmetic. In this manuscript we consider a v…
Ordinal notation systems corresponding to Friedman's linearized well-partial-orders with gap-condition
Michael Rathjen, Jeroen Van der Meeren, Andreas Weiermann
In this article we investigate whether the addition-free theta functions form a canonical notation system for the linear versions of Friedman's well-partial-orders with the so-call…