Metastability in the Furstenberg-Zimmer tower

• Autorzy: Jeremy Avigad , Henry Towsner
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 37A05: Measure-preserving transformations
• 03E15: Descriptive set theory
• 03F03: Proof theory, general

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 210
• Numer: 3
• Strony: 243-268

Daty

wydano

2010

Twórcy

autor

Jeremy Avigad

• Department of Philosophy, and Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.

autor

Henry Towsner

• Department of Mathematics, University of California, Los Angeles, CA 90095-1555, U.S.A.

Identyfikatory

DOI

10.4064/fm210-3-2