Infinite saturated orders

Details Infinite saturated orders Infinite saturated orders

2010-10-11

arxiv.org/abs/1010.2219v1

Mathematics

Logic

Accepted for publication in Order

Scientific paper

We generalize the notion of saturated order to infinite partial orders and give both a set-theoretic and an algebraic characterization of such orders. We then study the proof theoretic strength of the equivalence of these characterizations in the context of reverse mathematics, showing that depending on one's choice of definitions it is either provable in $\mathsf{RCA}_0$ or equivalent to $\mathsf{ACA}_0$.

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