Journal of Symbolic Logic

Lusin-Sierpinski Index for the Internal Sets

Bosko Zivaljevic

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183743898

Mathematical Reviews number (MathSciNet)
MR1150932

Zentralblatt MATH identifier
0753.03031

JSTOR
links.jstor.org

Citation

Zivaljevic, Bosko. Lusin-Sierpinski Index for the Internal Sets. J. Symbolic Logic 57 (1992), no. 1, 172--178. https://projecteuclid.org/euclid.jsl/1183743898


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