<abstract xmlns="http://www.w3.org/1999/xhtml"> We present a simple proof of a dichotomy theorem by Kechris- -Louveau-Woodin [Kechris, A. S., Louveau, A.: <italic>Descriptive set theory and the</italic><italic>structure of sets of uniqueness, </italic>London Math. Soc. Lecture Note Ser. <bold>128 </bold>(1987), 104-138] telling that every Π11<italic>σ</italic>-ideal of compact subsets of a Polish space is either G<italic>δ </italic>or else Π11 -complete.</abstract>

We present a simple proof of a dichotomy theorem by Kechris- -Louveau-Woodin [Kechris, A. S., Louveau, A.: Descriptive set theory and thestructure of sets of uniqueness, London Math. Soc. Lecture Note Ser. 128 (1987), 104-138] telling that every Π11σ-ideal of compact subsets of a Polish space is either Gδ or else Π11 -complete.

Application of Hurewicz theorem to classification of Π11 -complete sets

Institute of Mathematics University of P. J. ˇSaf´arik Jesenn´a 5 SK–040-01 Koˇsice SLOVAKIA

Tatra Mountains Mathematical Publications

Application of Hurewicz theorem to classification of Π -complete sets

We present a simple proof of a dichotomy theorem by Kechris- -Louveau-Woodin [Kechris, A. S., Louveau, A.: Descriptive set theory and thestructure of sets of...

Application of Hurewicz theorem to classification of Π₁¹ -complete sets

Published Online: Nov 13, 2012

Page range: 65 - 69

DOI: https://doi.org/10.2478/v10127-010-0020-y

Keywords
analytic set, coanalytic set, Π<sup>1</sup><sub>1</sub> -complete set, hyperspace, σ-ideal of compact sets, Hurewicz theorem.

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