대한수학회지 (Journal of the Korean Mathematical Society)

  • 제53권2호
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  • Pages.315-329
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  • 2016
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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SATURATED STRUCTURES FROM PROBABILITY THEORY

  • Song, Shichang (Department of Mathematics School of Science Beijing Jiaotong University)
  • 투고 : 2014.12.20
  • 발행 : 2016.03.01
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초록

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.

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참고문헌

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