19 citations · 101 across the 35 of their papers we have counts for
6 papers · 1 filter
Ackermann and Goodstein go functorial
Juan P. Aguilera, Anton Freund, Michael Rathjen +1
We present variants of Goodstein's theorem that are equivalent to arithmetical comprehension and to arithmetical transfinite recursion, respectively, over a weak base theory. These…
Well ordering principles and -statements: a pilot study
Anton Freund
In previous work, the author has shown that -induction along is equivalent to a suitable formalization of the statement that every normal function on the ordinal…
What is effective transfinite recursion in reverse mathematics?
Anton Freund
In the context of reverse mathematics, effective transfinite recursion refers to a principle that allows us to construct sequences of sets by recursion along arbitrary well orders,…
A mathematical commitment without computational strength
Anton Freund
We present a new manifestation of Gödel's second incompleteness theorem and discuss its foundational significance, in particular with respect to Hilbert's program. Specifically, we…
From Kruskal's theorem to Friedman's gap condition
Anton Freund
Harvey Friedman's gap condition on embeddings of finite labelled trees plays an important role in combinatorics (proof of the graph minor theorem) and mathematical logic (strong in…
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…