2 papers
math.LO2026
Free sets, thin sets and rainbows for barriers
Lorenzo Carlucci, Oriola Gjetaj
We formulate and prove the generalizations of Friedman's free set and thin set theorems and of the rainbow Ramsey theorem to colorings of barriers. We analyze the strength of these…
math.LO2026
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…