Infinite saturated orders

Damir D. Dzhafarov

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arXiv · 1010.2219

Infinite saturated orders

Damir D. Dzhafarov

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Abstract

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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BibTeX RIS

Damir D. Dzhafarov. 2010-10-11. Infinite saturated orders. https://arxiv.org/abs/1010.2219

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