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Sacks forcing collapses 𝔠 to 𝔟

Petr Simon (1993)

Commentationes Mathematicae Universitatis Carolinae

We shall prove that Sacks algebra is nowhere ( 𝔟 , 𝔠 , 𝔠 ) -distributive, which implies that Sacks forcing collapses 𝔠 to 𝔟 .

Selfduality of the system of convex subsets of a partially ordered set

Miron Zelina (1993)

Commentationes Mathematicae Universitatis Carolinae

For a partially ordered set P let us denote by C o P the system of all convex subsets of P . It is found the necessary and sufficient condition (concerning P ) under which C o P (as a partially ordered set) is selfdual.

Semilattices with sectional mappings

Ivan Chajda, Günther Eigenthaler (2007)

Discussiones Mathematicae - General Algebra and Applications

We consider join-semilattices with 1 where for every element p a mapping on the interval [p,1] is defined; these mappings are called sectional mappings and such structures are called semilattices with sectional mappings. We assign to every semilattice with sectional mappings a binary operation which enables us to classify the cases where the sectional mappings are involutions and / or antitone mappings. The paper generalizes results of [3] and [4], and there are also some connections to [1].

Semi-ordered groups

Jiří Rachůnek (1979)

Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika

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