An Ulm-Type Classification Theorem for Equivalence Relations in Solovay Model

Kanovei, Vladimir

J. Symbolic Logic, Tome 62 (1997) no. 1, p. 1333-1351 / Harvested from Project Euclid

Résumé

We prove that in the Solovay model, every OD equivalence relation, E, over the reals, either admits an OD reduction to the equality relation on the set of all countable (of length $< \omega_1$) binary sequences, or continuously embeds $\mathrm{E}_0$, the Vitali equivalence. If E is a $\Sigma^1_1$ (resp. $\Sigma^1_2$) relation then the reduction above can be chosen in the class of all $\triangle_1$ (resp. $\triangle_2$) functions. The proofs are based on a topology generated by OD sets.

Publié le : 1997-12-14
Classification:

@article{1183745385,
     author = {Kanovei, Vladimir},
     title = {An Ulm-Type Classification Theorem for Equivalence Relations in Solovay Model},
     journal = {J. Symbolic Logic},
     volume = {62},
     number = {1},
     year = {1997},
     pages = { 1333-1351},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745385}
}

Kanovei, Vladimir. An Ulm-Type Classification Theorem for Equivalence Relations in Solovay Model. J. Symbolic Logic, Tome 62 (1997) no. 1, pp.  1333-1351. http://gdmltest.u-ga.fr/item/1183745385/