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Remarks on measurable Boolean algebras and sequential cardinals

G. Plebauek (1993)

Fundamenta Mathematicae

The paper offers a generalization of Kalton-Roberts' theorem on uniformly exhaustive Maharam's submeasures to the case of arbitrary sequentially continuous functionals. Applying the result one can reduce the problem of measurability of sequential cardinals to the question whether sequentially continuous functionals are uniformly exhaustive.

Representing free Boolean algebras

Alan Dow, P. Nyikos (1992)

Fundamenta Mathematicae

Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with ℵ 1 generators is represented. It was shown in [2] that it is consistent that the free Boolean algebra of size continuum is not a subalgebra...

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 .

Stone Lattices

Adam Grabowski (2015)

Formalized Mathematics

The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the paper, the notion of a pseudocomplement in a lattice is formally introduced in Mizar, and based on this we define the notion of the skeleton and the set of dense elements in a pseudocomplemented lattice, giving the meet-decomposition of arbitrary element of a lattice as the infimum of two elements: one belonging to the skeleton, and the other which...

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