We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
${\mathsf {CAC\ FOR\ TREES}}$
${\mathsf {CAC\ for\ trees}}$ 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 statement 
$\mathsf {SHER}$ introduced by Dorais et al. [8], and the statement 
$\mathsf {TAC}+\mathsf {B}\Sigma ^0_2$ where 
$\mathsf {TAC}$ is the tree antichain theorem introduced by Conidis [6]. We show that 
${\mathsf {CAC\ for\ trees}}$ is computationally very weak, in that it admits probabilistic solutions.
