J. Korean Math. Soc. 2016; 53(2): 315-329
Printed March 1, 2016
https://doi.org/10.4134/JKMS.2016.53.2.315
Copyright © The Korean Mathematical Society.
Shichang Song
Beijing Jiaotong University
In the setting of continuous logic, we study atomless probability spaces and atomless random variable structures. We characterize $\kappa$-saturated atomless probability spaces and $\kappa$-saturated atomless random variable structures for every infinite cardinal $\kappa$. Moreover, $\kappa$-saturated and strongly $\kappa$-homogeneous atomless probability spaces and $\kappa$-saturated and strongly $\kappa$-homogeneous atomless random variable structures are characterized for every infinite cardinal $\kappa$. \!For atomless probability spaces, we prove that $\aleph_1$-saturation is equivalent to Hoover-Keisler saturation. For atomless random variable structures whose underlying probability spaces are Hoover-Keisler saturated, we prove several equivalent conditions.
Keywords: continuous logic, saturation, Maharam spectrum, probability algebras, random variables
MSC numbers: 03C50, 28A60
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