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## Fundamenta Mathematicae

2010 | 210 | 3 | 243-268
Tytuł artykułu

### Metastability in the Furstenberg-Zimmer tower

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EN
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EN
According to the Furstenberg-Zimmer structure theorem, every measure-preserving system has a maximal distal factor, and is weak mixing relative to that factor. Furstenberg and Katznelson used this structural analysis of measure-preserving systems to provide a perspicuous proof of Szemerédi's theorem. Beleznay and Foreman showed that, in general, the transfinite construction of the maximal distal factor of a separable measure-preserving system can extend arbitrarily far into the countable ordinals. Here we show that the Furstenberg-Katznelson proof does not require the full strength of the maximal distal factor, in the sense that the proof only depends on a combinatorial weakening of its properties. We show that this combinatorially weaker property obtains fairly low in the transfinite construction, namely, by the $ω^{ω^{ω}}$th level.
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Tom
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243-268
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wydano
2010
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autor
• Department of Philosophy, and Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
autor
• Department of Mathematics, University of California, Los Angeles, CA 90095-1555, U.S.A.
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