Authors: Farah, Ilijas 
Shelah, Saharon
Title: Rigidity of continuous quotients
Journal: Journal of the Institute of Mathematics of Jussieu
Volume: 15
Issue: 1
First page: 1
Last page: 28
Issue Date: 1-Jan-2016
Rank: M21
ISSN: 1474-7480
DOI: 10.1017/S1474748014000218
We study countable saturation of metric reduced products and introduce continuous fields of metric structures indexed by locally compact, separable, completely metrizable spaces. Saturation of the reduced product depends both on the underlying index space and the model. By using the Gelfand-Naimark duality we conclude that the assertion that the Stone-Čech remainder of the half-line has only trivial automorphisms is independent from ZFC (Zermelo-Fraenkel axiomatization of set theory with the Axiom of Choice). Consistency of this statement follows from the Proper Forcing Axiom, and this is the first known example of a connected space with this property.
Keywords: asymptotic sequence algebra | continuum hypothesis | countable saturation | Proper Forcing Axiom | Reduced products
Publisher: Cambridge University Press

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