Independent families on complete Boolean algebras
We study combinatorial properties of the partial order (Dense(ℚ),⊆). To do that we introduce cardinal invariants , , , , , describing properties of Dense(ℚ). These invariants satisfy ≤ ℚ ≤ ℚ ≤ ℚ ≤ ℚ ≤ ℚℚ = pℚ = tℚ = iℚ > hℚ > rnon(M)=min||: ⊆ Dense(R) ∧ (∀I ∈ nwd(R))(∃D ∈ )(I ∩ D = ∅) and cof(M) = min||: ⊆ Dense(ℚ) ∧ (∀I ∈ nwd)(∃D ∈ )(I ∩ = ∅). We use these facts to show that cof(M) ≤ i, which improves a result of S. Shelah.
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