Free Extensions of Sets of Boolean Algebras
نویسندگان
چکیده
منابع مشابه
Extensions of Free Boolean Algebras
In a series of papers [2, 3, 4, 5], B. Efimov has given sufficient conditions for a Boolean algebra to have a free subalgebra of given cardinality. For example, he has shown that if an infinite Boolean algebra A has cardinality greater than exp exp exp v, but the supremum of the cardinalities of subsets of disjoint elements in A is not greater than v, then A has a free subalgebra with (exp v) i...
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15 صفحه اولRepresenting free Boolean algebras
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It is shown that every uncountable Boolean algebra A contains an uncountable subset / such that no a of / is in the subalgebra generated by I\{a} using an additional axiom of set theory. It is also shown that a use of some such axiom is necessary. A subset / of a Boolean algebra A is irredundant if no proper subset of / generates the same subalgebra as /, or equivalently, if no a of / is in the...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1964
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(64)50060-8