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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 .

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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