Displaying similar documents to “Life in the Sacks model”

More results in polychromatic Ramsey theory

Uri Abraham, James Cummings (2012)

Open Mathematics

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We study polychromatic Ramsey theory with a focus on colourings of [ω 2]2. We show that in the absence of GCH there is a wide range of possibilities. In particular each of the following is consistent relative to the consistency of ZFC: (1) 2ω = ω 2 and ω 2 → p o l y ( α ) ℵ 0 - b d d 2 for every α <ω 2; (2) 2ω = ω 2 and ω 2 ↛ p o l y ( ω 1 ) 2 - b d d 2 .

Non-Glimm–Effros equivalence relations at second projective level

Vladimir Kanovei (1997)

Fundamenta Mathematicae

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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,...