Displaying similar documents to “Closure properties of countable non-standard integers”

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,...