19 citations · 101 across the 35 of their papers we have counts for
6 papers · 1 filter
Normal functions and maximal order types
Anton Freund, Davide Manca
Transformations of well partial orders induce functions on the ordinals, via the notion of maximal order type. In most examples from the literature, these functions are not normal,…
The uniform Kruskal theorem: between finite combinatorics and strong set existence
Anton Freund, Patrick Uftring
The uniform Kruskal theorem extends the original result for trees to general recursive data types. As shown by A. Freund, M. Rathjen and A. Weiermann, it is equivalent to -c…
On the logical strength of the better quasi order with three elements
Anton Freund
The notion of better quasi order (), due to Nash-Williams, is very fruitful mathematically and intriguing from the standpoint of logic, due to several long-standing o…
Higman's lemma is stronger for better quasi orders
Anton Freund
We prove that Higman's lemma is strictly stronger for better quasi orders than for well quasi orders, within the framework of reverse mathematics. In fact, we show a stronger resul…
Impredicativity and Trees with Gap Condition: A Second Course on Ordinal Analysis
Anton Freund
These lecture notes introduce central notions of impredicative ordinal analysis, such as the Bachmann-Howard ordinal and the method of collapsing, which transforms uncountable proo…
R.E. Bruck, proof mining and a rate of asymptotic regularity for ergodic averages in Banach spaces
Anton Freund, Ulrich Kohlenbach
We analyze a proof of Bruck to obtain an explicit rate of asymptotic regularity for Cesàro means in uniformly convex Banach spaces. Our rate will only depend on a norm bound and a…