Displaying similar documents to “Concerning certain minimal cover refineable spaces”

Minimality of non-σ-scattered orders

Tetsuya Ishiu, Justin Tatch Moore (2009)

Fundamenta Mathematicae

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We will characterize-under appropriate axiomatic assumptions-when a linear order is minimal with respect to not being a countable union of scattered suborders. We show that, assuming PFA⁺, the only linear orders which are minimal with respect to not being σ-scattered are either Countryman types or real types. We also outline a plausible approach to demonstrating the relative consistency of: There are no minimal non-σ-scattered linear orders. In the process of establishing these results,...