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Classification systems and their lattice

Sándor Radeleczki (2002)

Discussiones Mathematicae - General Algebra and Applications

We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent and...

Comparison of subset systems

Evelyn Nelson, Jiří Adámek, Andreas Jung, Jan Reiterman, Andrzej Tarlecki (1988)

Commentationes Mathematicae Universitatis Carolinae

Completion of partially ordered sets

Sergey A. Solovyov (2006)

Discussiones Mathematicae - General Algebra and Applications

The paper considers a generalization of the standard completion of a partially ordered set through the collection of all its lower sets.

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