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math.LO2016
"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…
math.LO2016
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…