4 papers
Reverse mathematics and dimension of posets
Alberto Marcone, Andrea Volpi
Order dimension theory measures the complexity of partially ordered sets by quantifying how far they are from being linearly ordered. In this paper we study classical bounding resu…
The strength of Ramsey's theorem for -large sets
Lorenzo Carlucci, Andrea Volpi, Konrad Zdanowski
We calibrate the reverse mathematical strength of a family of extensions of Ramsey's theorem to finite colorings of certain subsets of the natural numbers of unbounded finite dimen…
The barrier Ramsey theorem
Alberto Marcone, Antonio Montalbán, Andrea Volpi
In this paper we study a very general finite Ramsey theorem, where both the sets being colored and the homogeneous set must satisfy some largeness notion. For the homogeneous set t…
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…