7 papers
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…
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…