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Chains and antichains in Boolean algebras

M. Losada, Stevo Todorčević (2000)

Fundamenta Mathematicae

We give an affirmative answer to problem DJ from Fremlin’s list [8] which asks whether M A ω 1 implies that every uncountable Boolean algebra has an uncountable set of pairwise incomparable elements.

Characterization of posets of intervals

Judita Lihová (2000)

Archivum Mathematicum

If A is a class of partially ordered sets, let P ( A ) denote the system of all posets which are isomorphic to the system of all intervals of A for some A A . We give an algebraic characterization of elements of P ( A ) for A being the class of all bounded posets and the class of all posets A satisfying the condition that for each a A there exist a minimal element u and a maximal element v with u a v , respectively.

Characterizations of 0-distributive posets

Vinayak V. Joshi, B. N. Waphare (2005)

Mathematica Bohemica

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

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