Finite and countable families of algebras of sets
- Autores: L. S. Grinblat
- Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 4, 2010, págs. 613-623
- Idioma: inglés
- DOI: 10.4310/mrl.2010.v17.n4.a3
- Enlaces
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Resumen
Let $\{\A_\la\}_{\la \in \La}$ be a family of algebras of sets defined on a set $X, 0 < \# (\La) \leq \aleph_0$, and $\A_\la \neq \P(X)$ for each $\la \in \La$. We assume that $\A_\la$ are $\sigma$-algebras if $\# (\La) = \aleph_0$. We obtained the necessary and sufficient conditions for which $\bigcup_{\la \in \La} \A_\la = \P(X)$. In the formulation of these conditions we use $\omega$-saturated algebras and finite sequences of ultrafilters on $X$.
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