论文信息 - The basis problem for CCC posets

The basis problem for CCC posets

Given a family Σ of forcing notions a subfamily Σ0 of Σ is called a basis provided for every P ∈ Σ there is Q ∈ Σ0 such that forcing with P adds a generic for Q. We investigate the problem of finding a small basis for the class of nonatomic ccc partial orderings. Prikry conjectured that it is consistent that {C,R} forms such a basis, where C is Cohen forcing and R is random real forcing. We survey what is known about this problem and present some new results. Finally we list some open questions.

Boban Velickovic

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