10 citations · 13 across the 10 of their papers we have counts for
11 papers
An equivalent form of Hindman's Theorem
Lorenzo Carlucci, Andrea D'Amico
We prove the equivalence of Hindman's finite sums theorem with a natural extension of Ramsey's theorem.
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…
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…
Regressive versions of Hindman's Theorem
Lorenzo Carlucci, Leonardo Mainardi
When the Canonical Ramsey's Theorem by Erdős and Rado is applied to regressive functions one obtains the Regressive Ramsey's Theorem by Kanamori and McAloon. Taylor proved a "canon…
The adjacent Hindman's theorem for uncountable groups
Lorenzo Carlucci, David J. Fernández-Bretón
Recent results of Hindman, Leader and Strauss and of the second author and Rinot showed that some natural analogs of Hindman's Theorem fail for all uncountable cardinals. Results i…
A note on Hindman-type theorems for uncountable cardinals
Lorenzo Carlucci
Recent results of Hindman, Leader and Strauss and of Fernández-Bretón and Rinot showed that natural versions of Hindman's Theorem fail {\em for all} uncontable cardinals. On the ot…
New bounds on the strength of some restrictions of Hindman's Theorem
Lorenzo Carlucci, Leszek Aleksander Kołodziejczyk, Francesco Lepore +1
We prove upper and lower bounds on the effective content and logical strength for a variety of natural restrictions of Hindman's Finite Sums Theorem. For example, we show that Hind…
"Weak yet strong" restrictions of Hindman's Finite Sums Theorem
Lorenzo Carlucci
We present a natural restriction of Hindman's Finite Sums Theorem that admits a simple combinatorial proof (one that does not also prove the full Finite Sums Theorem) and low compu…
A weak variant of Hindman's Theorem stronger than Hilbert's Theorem
Lorenzo Carlucci
Hirst investigated a slight variant of Hindman's Finite Sums Theorem -- called Hilbert's Theorem -- and proved it equivalent over $\RCA_0$ to the Infinite Pigeonhole Principle for…
The strength of Ramsey Theorem for coloring relatively large sets
Lorenzo Carlucci, Konrad Zdanowski
We characterize the computational content and the proof-theoretic strength of a Ramsey-type theorem for bi-colorings of so-called {\em exactly large} sets. An {\it exactly large} s…
Unprovability results involving braids
Lorenzo Carlucci, Patrick Dehornoy, Andreas Weiermann
We construct long sequences of braids that are descending with respect to the standard order of braids (``Dehornoy order''), and we deduce that, contrary to all usual algebraic pro…