In smooth/C^{1,1} Lorentzian spacetimes, future/past chrono- and causalcompleteness and bounded directed order completeness are all equivalent to global hyperbolicity.
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Global hyperbolicity meets order completeness
In smooth/C^{1,1} Lorentzian spacetimes, future/past chrono- and causalcompleteness and bounded directed order completeness are all equivalent to global hyperbolicity.