Geodesic
Non-Glimm–Effros equivalence relations at second projective level
Fundamenta Mathematicae, Tome 154 (1997) no. 1, pp. 1-35

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A model is presented in which the $Σ^1_2$ 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 ${Π}^1_2$ non-Glimm-Effros equivalence relation on reals. As a more elementary application of the technique of "ill"founded Sacks iterations, we obtain a model in which every nonconstructible real codes a collapse of a given cardinal $κ ≥ ℵ_2^{old}$ to $ℵ_1^{old}$.
DOI : 10.4064/fm-154-1-1-35

Vladimir Kanovei 1

1 
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Vladimir Kanovei. Non-Glimm–Effros equivalence relations at second projective level. Fundamenta Mathematicae, Tome 154 (1997) no. 1, pp. 1-35. doi: 10.4064/fm-154-1-1-35

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