Reverse Mathematics and Partial Orders
نویسنده
چکیده
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 wellknown 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 (for instance showing that the statement is provable in WKL0 but not in WWKL0).
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