ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D2149
Lambda algebra
Formulation 0
Let $X$ be a D11: Set.
A D11: Set $\Lambda \subseteq \mathcal{P}(X)$ is a Lambda algebra on $X$ if and only if
(1) \begin{equation} X \in \Lambda \end{equation}
(2) \begin{equation} \forall \, E, F \in \Lambda \left( E \subseteq F \quad \implies \quad F \setminus E \in \Lambda \right) \end{equation}
(3) \begin{equation} \forall \, E_0, E_1, E_2, \dots \in \Lambda \left( E_0 \subseteq E_1 \subseteq E_2 \subseteq \dots \quad \implies \quad \bigcup_{n \in \mathbb{N}} E_n \in \Lambda \right) \end{equation}