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Subjects
03-XX Mathematical logic and foundations
03Exx Set theory
03E40 Other aspects of forcing and Boolean-valued models

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Nonexistence of nonmolecular generic sets.

Steiner, Donald D., Abian, Alexander (1984)

Publications de l'Institut Mathématique. Nouvelle Série

Non-Glimm–Effros equivalence relations at second projective level

Vladimir Kanovei (1997)

Fundamenta Mathematicae

A model is presented in which the $Σ_{2}^{1}$ equivalence relation xCy iff L[x]=L[y] of equiconstructibility of reals does not admit a reasonable form of the Glimm-Effros theorem. The model is a kind of iterated Sacks generic extension of the constructible model, but with an “ill“founded “length” of the iteration. In another model of this type, we get an example of a $Π_{2}^{1}$ non-Glimm-Effros equivalence relation on reals. As a more elementary application of the technique of “ill“founded Sacks iterations, we obtain...

Norms on possibilities. II: More ccc ideals on $2^{ω}$ .

Rosłanowski, Andrzej, Shelah, Saharon (1997)

Journal of Applied Analysis

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