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Sacks forcing; Cohen real; disjoint refinement
We prove that if there exists a Cohen real over a model, then the family of perfect sets coded in the model has a disjoint refinement by perfect sets.
[1] Balcar B., Simon P.: Disjoint refinement. in: Handbook of Boolean Algebras2 J.D. Monk and R. Bonnet North-Holland Amsterdam (1989), 334-386. MR 0991597
[2] Judah H., Miller A. W., Shelah S.: Sacks forcing, Laver forcing, and Martin's axiom. Arch. Math. Logic 31 (1992), 145-161. MR 1147737 | Zbl 0755.03026
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