Perfect subsets of invariant CA-sets

The familiar theorem that any ₂¹(a)-set X of real numbers (where a is a fixed real parameter) not containing a perfect kernel necessarily satisfies the condition XL[a] is extended to a wider class of sets, with countable ordinals allowed as additional parameters in ₂¹(a)-definitions.Translated from Matematicheskie Zametki, vol. 77, no. 3, 2005, pp. 334–338.Original Russian Text Copyright © 2005 by V. G. Kanovei, V. A. Lyubetskii.This revised version was published online in April 2005 with a corrected issue number.