Journal of Symbolic Logic

Lusin-Sierpinski Index for the Internal Sets

Bosko Zivaljevic

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We prove that there exists a function $f$ which reduces a given $\Pi^1_1$ subset $P$ of an internal set $X$ of an $\omega_1$-saturated nonstandard universe to the set $\mathbf{WF}$ 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 $\Pi^1_1$ but not $\Sigma^1_1$ set is given.

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J. Symbolic Logic, Volume 57, Issue 1 (1992), 172-178.

First available in Project Euclid: 6 July 2007

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Zivaljevic, Bosko. Lusin-Sierpinski Index for the Internal Sets. J. Symbolic Logic 57 (1992), no. 1, 172--178.

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