Non-Glimm–Effros equivalence relations at second projective level

Kanovei, Vladimir

Fundamenta Mathematicae, Tome 154 (1997), p. 1-35 / Harvested from The Polish Digital Mathematics Library

Résumé

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 a model in which every nonconstructible real codes a collapse of a given cardinal $κ \geq ℵ_{2}^{o l d}$ to $ℵ_{1}^{o l d}$ .

Publié le : 1997-01-01

Zbl 0883.03034

EUDML-ID : urn:eudml:doc:212225

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     author = {Vladimir Kanovei},
     title = {Non-Glimm--Effros equivalence relations at second projective level},
     journal = {Fundamenta Mathematicae},
     volume = {154},
     year = {1997},
     pages = {1-35},
     zbl = {0883.03034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv154i1p1bwm}
}

Kanovei, Vladimir. Non-Glimm–Effros equivalence relations at second projective level. Fundamenta Mathematicae, Tome 154 (1997) pp. 1-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv154i1p1bwm/

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