Life in the Sacks model

Michael Hrušák

Displaying similar documents to “Life in the Sacks model”

Mutually generic classes and incompatible expansions

Matt Kaufmann (1984)

Fundamenta Mathematicae

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Uncountable β-models with countable height

Wojciech Guzicki (1974)

Fundamenta Mathematicae

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On the groupwise density number for filters

Heike Mildenberger (2005)

Acta Universitatis Carolinae. Mathematica et Physica

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Sacks reals and Martin's axiom

Tim Carlson, Richard Laver (1989)

Fundamenta Mathematicae

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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 $ω_{2} \to^{p o l y} {(α)}_{ℵ_{0} - b d d}^{2}$ for every α <ω 2; (2) 2ω = ω 2 and $ω_{2} ↛^{p o l y} {(ω_{1})}_{2 - b d d}^{2}$ .

Forcing with proper classes

Andrzej Zarach (1973)

Fundamenta Mathematicae

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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,...