Nonstandard methods characterize the weak, strong, and mixed extensions of arbitrary relations to ultrafilter spaces and their interplay.
Divisibility orders in $\beta N$
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abstract
We consider five divisibility orders on the Stone-\v{C}ech compactification $\beta N$. We find antichains of incompatible elements, and characterize maximal and minimal elements. The main result shows that two of these relations, $\mid_L$ and $\mid_{LN}$, are strictly stronger than the Rudin-Keisler order.
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2025 1verdicts
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Weak, strong and mixed extensions of relations to spaces of ultrafilters
Nonstandard methods characterize the weak, strong, and mixed extensions of arbitrary relations to ultrafilter spaces and their interplay.