5 papers
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…
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 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 KÅnig's lemma
Anton Freund, Patrick Uftring
We prove conservativity results for weak KÅnig's lemma that extend the celebrated result of Harrington (for -statements) and are somewhat orthogonal to the extension by Si…