ThmDex – An index of mathematical definitions, results, and conjectures.
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Deduction system
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Zermelo-Fraenkel set theory
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Subsigma-algebra
Definition D3344
Set of subsigma-algebras
Formulation 0
Let $X$ be a D11: Set such that
(i) $\mathsf{SA} = \mathsf{SA}(X)$ is the D484: Set of sigma-algebras on $X$
(ii) $\mathcal{F} \in \mathsf{SA}$ is a D84: Sigma-algebra on $X$
The set of subsigma-algebras of $\mathcal{F}$ on $X$ is the D11: Set \begin{equation} \{ \mathcal{G} \in \mathsf{SA} : \mathcal{G} \subseteq \mathcal{F} \} \end{equation}