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Article

Zapletal, Jindřich
Separating equivalence classes. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 59 (2018), issue 4, pp. 531-540
MSC: 03E15, 03E17 | MR 3914719 | Zbl 06997369 | DOI: 10.14712/1213-7243.2015.267
Keywords:
countable Borel equivalence relation; forcing
Summary:
Given a countable Borel equivalence relation, I introduce an invariant measuring how difficult it is to find Borel sets separating its equivalence classes. I evaluate these invariants in several standard generic extensions.
References:
[1] Jech T.: Set Theory. Springer Monographs in Mathematics, Springer, Berlin, 2003. MR 1940513 | Zbl 1007.03002
[2] Kanovei V.: Borel Equivalence Relations: Structure and Classification. University Lecture Series, 44, American Mathematical Society, Providence, 2008. DOI 10.1090/ulect/044/06 | MR 2441635
[3] Zapletal J.: Forcing Idealized. Cambridge Tracts in Mathematics, 174, Cambridge University Press, Cambridge, 2008. MR 2391923 | Zbl 1140.03030
[4] Zapletal J.: Hypergraphs and proper forcing. available at arXiv:1710.10650 [math.LO] (2017), 64 pages.
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