3 citations · 6 across the 9 of their papers we have counts for
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Avoiding logical strength in real analysis
Anton Freund, Nicholas Pischke, Patrick Uftring
In reverse mathematics, real numbers are traditionally represented by Cauchy sequences with a given rate of convergence. We work without rates and speak of slow Cauchy sequences. I…
Maximal order types for sequences with gap condition
Patrick Uftring
Higman's lemma states that for any well partial order , the partial order of finite sequences with members from is also well. By combining results due to Girard as wel…
The uniform Kruskal theorem over RCA
Patrick Uftring
Kruskal's theorem famously states that finite trees (ordered using an infima-preserving embeddability relation) form a well partial order. Freund, Rathjen, and Weiermann extended t…
More conservativity for weak Kőnig's lemma
Anton Freund, Patrick Uftring
We prove conservativity results for weak Kőnig's lemma that extend the celebrated result of Harrington (for -statements) and are somewhat orthogonal to the extension by Simp…
On inverse Goodstein sequences
Patrick Uftring
In the late 1980s, Abrusci, Girard and van de Wiele defined a variant of Goodstein sequences: the so-called inverse Goodstein sequence. In their work, they show that it terminates…
Weihrauch degrees without roots
Patrick Uftring
We answer the following question by Arno Pauly: "Is there a square-root operator on the Weihrauch degrees?". In fact, we show that there are uncountably many pairwise incomparable…
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…
Weak and Strong Versions of Effective Transfinite Recursion
Patrick Uftring
Working in the context of reverse mathematics, we give a fine-grained characterization result on the strength of two possible definitions for Effective Transfinite Recursion used i…
The characterization of Weihrauch reducibility in systems containing E-PA + QF-AC
Patrick Uftring
We characterize Weihrauch reducibility in E-PA + QF-AC and all systems containing it by the provability in a linear variant of the same calculus using modifications of…