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Equivalences generated by families of Borel sets

Author: John P. Burgess
Journal: Proc. Amer. Math. Soc. 69 (1978), 323-326
MSC: Primary 04A25
MathSciNet review: 0476524
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Abstract: The equivalence relation on the reals generated by a family of $ {\aleph _\alpha }$ Borel sets has either $ \leqslant {\aleph _\alpha }$ or else exactly $ {2^{{\aleph _0}}}$ equivalence classes.

References [Enhancements On Off] (What's this?)

  • [1] J. P. Burgess, Infinitary languages and descriptive set theory, Doctoral Dissertation, Univ. of California, Berkeley, Calif., 1974.
  • [2] -, A reflection phenomenon in descriptive set theory, Fund. Math. (to appear). MR 551663 (81i:04002)
  • [3] K. Kuratowski, Topology, Vol. 1, Academic Press, New York, 1966. MR 0217751 (36:840)
  • [4] J. H. Silver, $ \Pi _1^1$ equivalence relations (to appear). MR 568914 (81d:03051)
  • [5] V. Harnik and M. Makkai, A tree argument in infinitary model theory, Proc. Amer. Math. Soc. 67 (1977), 309-314. MR 0472506 (57:12204)

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