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Article Dans Une Revue The Journal of Symbolic Logic Année : 2023

The Reverse Mathematics of CAC for trees

Résumé

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 TAC for trees is robust, that is, there exist several characterizations, some of which already appear in the literature, namely, the tree antichain theorem (TCAC) introduced by Conidis, and the statement SHER introduced by Dorais et al. We show that CAC for trees is computationally very weak, in that it admits probabilistic solutions.
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Dates et versions

hal-04093397 , version 1 (10-05-2023)

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Julien Cervelle, William Gaudelier, Ludovic Patey. The Reverse Mathematics of CAC for trees. The Journal of Symbolic Logic, In press, ⟨10.1017/jsl.2023.27⟩. ⟨hal-04093397⟩
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