19 citations · 101 across the 35 of their papers we have counts for
6 papers · 1 filter
Well ordering principles for iterated -comprehension
Anton Freund, Michael Rathjen
We introduce ordinal collapsing principles that are inspired by proof theory but have a set theoretic flavor. These principles are shown to be equivalent to iterated -compre…
Reverse mathematics of a uniform Kruskal-Friedman theorem
Anton Freund
The Kruskal-Friedman theorem asserts: in any infinite sequence of finite trees with ordinal labels, some tree can be embedded into a later one, by an embedding that respects a cert…
Unprovability in Mathematics: A First Course on Ordinal Analysis
Anton Freund
These are the lecture notes of an introductory course on ordinal analysis. Our selection of topics is guided by the aim to give a complete and direct proof of a mathematical indepe…
Bounds for a nonlinear ergodic theorem for Banach spaces
Anton Freund, Ulrich Kohlenbach
We extract quantitative information (specifically, a rate of metastability in the sense of Terence Tao) from a proof due to Kazuo Kobayasi and Isao Miyadera, which shows strong con…
Bachmann-Howard Derivatives
Anton Freund
It is generally accepted that H. Friedman's gap condition is closely related to iterated collapsing functions from ordinal analysis. But what precisely is the connection? We offer…
Patterns of resemblance and Bachmann-Howard fixed points
Anton Freund
Timothy Carlson's patterns of resemblance employ the notion of -elementarity to describe large computable ordinals. It has been conjectured that a relativization of these patt…