46 citations · 63 across the 10 of their papers we have counts for
16 papers
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…
Effectiveness and strong graph indivisibility
Damir D. Dzhafarov, Reed Solomon, Andrea Volpi
A relational structure is \emph{strongly indivisible} if for every partition , the induced substructure on or is isomorphic to . Camero…
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…
Lowness for isomorphism, countable ideals, and computable traceability
Johanna N. Y. Franklin, Reed Solomon
We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair const…
Model completeness and relative decidability
Jennifer Chubb, Russell Miller, Reed Solomon
We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model $\mathcal A…
The determined property of Baire in reverse math
Eric P. Astor, Damir Dzhafarov, Antonio Montalbán +2
We define the notion of a determined Borel code in reverse math, and consider the principle , which states that every determined Borel set has the property of Baire. We show t…
The reverse mathematics of Hindman's theorem for sums of exactly two elements
Barbara F. Csima, Damir D. Dzhafarov, Denis R. Hirschfeldt +3
Hindman's Theorem (HT) states that for every coloring of with finitely many colors, there is an infinite set such that all nonempty sums of dist…
Effectiveness for the Dual Ramsey Theorem
Damir Dzhafarov, Stephen Flood, Reed Solomon +1
We analyze the Dual Ramsey Theorem for partitions and colors () in the context of reverse math, effective analysis, and strong reductions. Over $\ma…
The uniform content of partial and linear orders
Eric P. Astor, Damir D. Dzhafarov, Reed Solomon +1
The principle asserts that every linear order on has an infinite ascending or descending sequence. This has been studied extensively in the reverse mathematics literature…
Effectiveness of Hindman's theorem for bounded sums
Damir D. Dzhafarov, Carl G. Jockusch, Reed Solomon +1
We consider the strength and effective content of restricted versions of Hindman's Theorem in which the number of colors is specified and the length of the sums has a specified fin…
Ramsey's theorem for singletons and strong computable reducibility
Damir D. Dzhafarov, Ludovic Patey, Reed Solomon +1
We answer a question posed by Hirschfeldt and Jockusch by showing that whenever , Ramsey's theorem for singletons and -colorings, , is not strongly co…
Lowness notions, measure and domination
Bjørn Kjos-Hanssen, Joseph S. Miller, Reed Solomon
We show that positive measure domination implies uniform almost everywhere domination and that this proof translates into a proof in the subsystem WWKL (but not in RCA) of…
Self-embeddings of computable trees
Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman +2
We divide the class of infinite computable trees into three types. For the first and second types, computes a nontrivial self-embedding while for the third type computes…
On a conjecture of Dobrinen and Simpson concerning almost everywhere domination
Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman +1
The notions of almost everywhere (a.e.) domination and its uniform version were introduced and studied in reverse mathematics. This paper studies these notions from a recursion-the…
Separating principles below Ramsey's Theorem for Pairs
Manuel Lerman, Reed Solomon, Henry Towsner
In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from $\RT$, Ramsey's Theorem for Pa…
Reverse mathematics and infinite traceable graphs
Peter Cholak, David Galvin, Reed Solomon
This paper falls within the general program of investigating the proof theoretic strength (in terms of reverse mathematics) of combinatorial principals which follow from versions o…