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2 results

Why Solovay real produces Cohen real
Janusz Pawlikowski
Journal:

The Journal of Symbolic Logic / Volume 51 / Issue 4 / December 1986

Published online by Cambridge University Press:

12 March 2014, pp. 957-968

Print publication:

December 1986
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An explanation is given of why, after adding to a model M of ZFC first a Solovay real r and next a Cohen real c, in M[r] [c] a Cohen real over M[c] is produced. It is also shown that a Solovay algebra iterated with a Cohen algebra can be embedded into a Cohen algebra iterated with a Solovay algebra.

On ideals of subsets of the plane and on Cohen reals
Jacek Cichoń, Janusz Pawlikowski
Journal:

The Journal of Symbolic Logic / Volume 51 / Issue 3 / September 1986

Published online by Cambridge University Press:

12 March 2014, pp. 560-569

Print publication:

September 1986
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Let be any proper ideal of subsets of the real line R which contains all finite subsets of R. We define an ideal * ∣ as follows: X ∈ * ∣ if there exists a Borel set B ⊂ R × R such that X ⊂ B and for any x ∈ R we have {y ∈ R: 〈x, y〉 ∈ B} ∈ . We show that there exists a family ⊂ * ∣ of power ω1 such that ⋃ ∉ * ∣ .
In the last section we investigate properties of ideals of Lebesgue measure zero sets and meager sets in Cohen extensions of models of set theory.