Title: New bounds on the strength of some restrictions of Hindman's Theorem,
Abstract: 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 Hindman's Theorem for sums of length at most 2 and 4
colors implies $\mathsf{ACA}_0$. An emerging {\em leitmotiv} is that the known
lower bounds for Hindman's Theorem and for its restriction to sums of at most 2
elements are already valid for a number of restricted versions which have
simple proofs and better computability- and proof-theoretic upper bounds than
the known upper bound for the full version of the theorem. We highlight the
role of a sparsity-like condition on the solution set, which we call apartness.