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August 2022 Model-Theoretic Properties of Dynamics on the Cantor Set
Christopher J. Eagle, Alan Getz
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Notre Dame J. Formal Logic 63(3): 357-371 (August 2022). DOI: 10.1215/00294527-2022-0022

Abstract

We examine topological dynamical systems on the Cantor set from the point of view of the continuous model theory of commutative C*-algebras. After some general remarks, we focus our attention on the generic homeomorphism of the Cantor set, as constructed by Akin, Glasner, and Weiss. We show that this homeomorphism is the prime model of its theory. We also show that the notion of “generic” used by Akin, Glasner, and Weiss is distinct from the notion of “generic” encountered in Fraïssé theory.

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Christopher J. Eagle. Alan Getz. "Model-Theoretic Properties of Dynamics on the Cantor Set." Notre Dame J. Formal Logic 63 (3) 357 - 371, August 2022. https://doi.org/10.1215/00294527-2022-0022

Information

Received: 9 December 2021; Accepted: 26 April 2022; Published: August 2022
First available in Project Euclid: 25 September 2022

Digital Object Identifier: 10.1215/00294527-2022-0022

Subjects:
Primary: 03C10
Secondary: 03C66 , 03C98 , ‎37B05‎ , 46J10 , 54C35‎

Keywords: Cantor set , Continuous logic , generic homeomorphism , model companion , odometer

Rights: Copyright © 2022 University of Notre Dame

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Vol.63 • No. 3 • August 2022
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