It is shown that under GCH every poset preserves its cofinality in any cofinality preserving extension. On the other hand, starting with measurable cardinals, a model with a part...
It is known that the "pattern containment" order on permutations is not a partial well-order. Nevertheless, many naturally defined subsets of permutations are partially ...
We constructively prove that the partially ordered set of finite permutations ordered by deletion of entries contains an infinite antichain. In other words, there exists an infini...
The C-subfunction relations on the set of functions on a finite base set A defined by function classes C are examined. For certain clones C on A, it is determined whether the part...