Real Analysis Exchange

On the parametric limit superior of a sequence of analytic sets.

Szymon Głab

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Abstract

Let $A_x$ stand for $x$-section of a set $A\subset2^\omega\times2^\omega$. We prove that any sequence $A_j\subset2^\omega\times2^\omega$, $j\in\omega$ of analytic sets, with uncountable $\limsup_{j\in H}A_x^j$ for all $x\in2^\omega$ and $H\in [\omega]^\omega$ admits a perfect set $P\subset2^\omega$ and $H\subset [\omega]^\omega$ with uncountable $\bigcap_{j\in H}A_x^j$ for all $x\in P$. This is a parametric version of the Komjath theorem [2].

Article information

Source
Real Anal. Exchange, Volume 31, Number 1 (2005), 285-290.

Dates
First available in Project Euclid: 5 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149516815

Mathematical Reviews number (MathSciNet)
MR2218843

Zentralblatt MATH identifier
1094.03032

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05]
Secondary: 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]

Keywords
analytic set Borel set parametrized Ellentuck theorem

Citation

Głab, Szymon. On the parametric limit superior of a sequence of analytic sets. Real Anal. Exchange 31 (2005), no. 1, 285--290. https://projecteuclid.org/euclid.rae/1149516815


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