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When does the Katětov order imply that one ideal extends the other?

Paweł Barbarski; Rafał Filipów; Nikodem Mrożek; Piotr Szuca — 2013

Colloquium Mathematicae

We consider the Katětov order between ideals of subsets of natural numbers (" $\leq_{K}$ ") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals for which $\leq_{K} \Rightarrow ⊑$ for every ideal . We find examples of ideals with this property and show how this property can be used to reformulate some problems known from the literature in terms of the Katětov order instead of the order "⊑ " (and vice versa).

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