11 citations · 35 across the 26 of their papers we have counts for
32 papers · 1 filter
The weakness of typicality
Eric P. Astor, Laurent Bienvenu, Damir Dzhafarov +4
Many statements studied in reverse mathematics can be seen as mathematical problems, formulated in terms of instances and solutions. We develop a framework of typicality encompassi…
The Ginsburg--Sands theorem and computability theory
Heidi Benham, Andrew De Lapo, Damir Dzhafarov +2
The Ginsburg--Sands theorem from topology states that every infinite topological space has an infinite subspace homeomorphic to exactly one of the following five topologies on :…
The tree pigeonhole principle in the Weihrauch degrees
Damir Dzhafarov, Reed Solomon, Manlio Valenti
We study versions of the tree pigeonhole principle, , in the context of Weihrauch-style computable analysis. The principle has previously been the subject of extensi…
On the first-order parts of problems in the Weihrauch degrees
Damir D. Dzhafarov, Reed Solomon, Keita Yokoyama
We introduce the notion of the \emph{first-order part} of a problem in the Weihrauch degrees. Informally, the first-order part of a problem is the strongest problem wi…
Reduction games, provability, and compactness
Damir D. Dzhafarov, Denis R. Hirschfeldt, Sarah C. Reitzes
Hirschfeldt and Jockusch (2016) introduced a two-player game in which winning strategies for one or the other player precisely correspond to implications and non-implications betwe…
Milliken's tree theorem and its applications: a computability-theoretic perspective
Paul-Elliot Anglès d'Auriac, Peter A. Cholak, Damir D. Dzhafarov +2
Milliken's tree theorem is a deep result in combinatorics that generalizes a vast number of other results in the subject, most notably Ramsey's theorem and its many variants and co…