5 papers
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…
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…
Predicative collapsing principles
Anton Freund
We show that arithmetical transfinite recursion is equivalent to a suitable formalization of the following: For every ordinal there exists an ordinal such that $1+β\cdot(β+…