Lusin-sierpiński index for the internal sets

Journal of Symbolic Logic 57 (1):172-178 (1992)
Abstract
We prove that there exists a function f which reduces a given Π1 1 subset P of an internal set X of an ω1-saturated nonstandard universe to the set WF of well-founded trees possessing properties similar to those possessed by the standard part map. We use f to define the Lusin-Sierpinski index of points in X, and prove the basic properties of that index using the classical properties of the Lusin-Sierpinski index. An example of a Π1 1 but not Σ1 1 set is given
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