Abstract:${\mathsf {CAC\ for\ trees}}$
is the statement asserting that any infinite subtree of
$\mathbb {N}^{<\mathbb {N}}$
has an infinite path or an infinite antichain. In this paper, we study the computational strength of this theorem from a reverse mathematical viewpoint. We prove that
${\mathsf {CAC\ for\ trees}}$
is robust, that is, there exist several characterizations, some of which already appear in the literature, namely, the statem… Show more
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