Independent complete subalgebras of collapsing algebras
Martin Gavalec (1981)
Colloquium Mathematicae
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Martin Gavalec (1981)
Colloquium Mathematicae
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Lutz Heindorf (1996)
Commentationes Mathematicae Universitatis Carolinae
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We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.
Aleksander Błaszczyk, Andrzej Kucharski, Sławomir Turek (2014)
Open Mathematics
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The aim of this paper is to show that every infinite Boolean algebra which admits a countable minimally acting group contains a dense projective subalgebra.
Brian Wynne (2008)
Fundamenta Mathematicae
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Two Boolean algebras are elementarily equivalent if and only if they satisfy the same first-order statements in the language of Boolean algebras. We prove that every Boolean algebra is elementarily equivalent to the algebra of clopen subsets of a normal P-space.
Roman Sikorski (1961)
Colloquium Mathematicum
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Janusz Czelakowski (1981)
Colloquium Mathematicae
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Saharon Shelah (1996)
Fundamenta Mathematicae
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We deal with Boolean algebras and their cardinal functions: π-weight π and π-character πχ. We investigate the spectrum of π-weights of subalgebras of a Boolean algebra B. Next we show that the π-character of an ultraproduct of Boolean algebras may be different from the ultraproduct of the π-characters of the factors.