Embedding Cohen algebras using pcf theory
Using a theorem from pcf theory, we show that for any singular cardinal ν, the product of the Cohen forcing notions on κ, κ < ν, adds a generic for the Cohen forcing notion on .
Examples for Souslin forcing
We give several examples of Souslin forcing notions. For instance, we show that there exists a proper analytical forcing notion without ccc and with no perfect set of incompatible elements, we give an example of a Souslin ccc partial order without the Knaster property, and an example of a totally nonhomogeneous Souslin forcing notion.
Exhaustive zero-convergence structures on Boolean algebras
Existence of non measurable sets
Extensions with the approximation and cover properties have no new large cardinals
If an extension V ⊆ V̅ satisfies the δ approximation and cover properties for classes and V is a class in V̅, then every suitably closed embedding j: V̅ → N̅ in V̅ with critical point above δ restricts to an embedding j ↾ V amenable to the ground model V. In such extensions, therefore, there are no new large cardinals above δ. This result extends work in [Ham01].