Objets algébriquement clos et injectifs dans les catégories localement présentables
On a weak Kelley-Morse theory of classes
On projectional skeletons in Vašák spaces
We provide an alternative proof of the theorem saying that any Vašák (or, weakly countably determined) Banach space admits a full -projectional skeleton. The proof is done with the use of the method of elementary submodels and is comparably simple as the proof given by W. Kubiś (2009) in case of weakly compactly generated spaces.
On sets with rank one in simple homogeneous structures
We study definable sets D of SU-rank 1 in , where ℳ is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a ’canonically embedded structure’, which inherits all relations on D which are definable in , and has no other definable relations. Our results imply that if no relation symbol of the language of ℳ has arity higher than 2, then there is a close relationship between triviality of dependence and being a reduct of a binary...