Reverse mathematics and partial orders

We investigate the reverse mathematics of several theorems about partial orders. We mainly focus on the analysis of scattered (no copy of the rationals) and FAC (no infinite antichains) partial orders, for which we consider many characterization theorems (for instance the well-known Hausdorff’s theorem for scattered linear orders). We settle the proof-theoretic strength of most of these theorems. If not, we provide positive and negative bounds.