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In this paper we examine the reverse mathematical strength of a variation ofHindman's Theorem HT constructed by essentially combining HT with the Thin SetTheorem TS to obtain a principle which we call thin-HT. thin-HT says that everycoloring $c: \mathbb{N} \to \mathbb{N}$ has an infinite set $S \subseteq\mathbb{N}$ whose finite sums are thin for $c$, meaning that there is an $i$with $c(s) \neq i$ for all $s \in S$. We show that there is a computableinstance of thin-HT such that every solution computes $\emptyset'$, as is thecase with HT (see Blass, Hirst, and Simpson 1987). In analyzing this proof, wededuce that thin-HT implies $ACA_0$ over $RCA_0 + I\Sigma^0_2$. On the otherhand, using Rumyantsev and Shen's computable version of the Lov\'asz LocalLemma, we show that there is a computable instance of the restriction ofthin-HT to sums of exactly 2 elements such that any solution has diagonallynoncomputable degree relative to $\emptyset'$. Hence there is a computableinstance of this restriction of thin-HT with no $\Sigma^0_2$ solution.

Thin Set Versions of Hindman's Theorem