Ramsey's Theorem [166] captures the idea that total disorder is impossible: a sufficiently
large structure will always contain a large ordered substructure. A well-known special case …

Weihrauch Complexity in Computable Analysis Page 1 Chapter 11 Weihrauch Complexity in
Computable Analysis Vasco Brattka, Guido Gherardi and Arno Pauly Abstract We provide a …

When we set out to write this book in the spring of 2011, the only introduction to reverse
mathematics was Simpson's Subsystems of Second Order Arithmetic [288]. Our motivation …

In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more
precisely, a natural extension for multi-valued functions on represented spaces. We call the …

We study closed choice principles for different spaces. Given information about what does
not constitute a solution, closed choice determines a solution. We show that with closed …

§ 1. Introduction. For most of its history, mathematics was algorithmic in nature. The
geometric claims in Euclid's Elements fall into two distinct categories:“problems,” which …

We classify the computational content of the Bolzano–Weierstraß Theorem and variants
thereof in the Weihrauch lattice. For this purpose we first introduce the concept of a …

Several notions of computability-theoretic reducibility between Π 2 1 principles have been
studied. This paper contributes to the program of analyzing the behavior of versions of …

We investigate the topological aspects of some algebraic computation models, in particular
the BSS-model. Our results can be seen as bounds on how different BSS-computability and …

We introduce two new operations (compositional products and implication) on Weihrauch
degrees, and investigate the overall algebraic structure. The validity of the various …