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- W2116785398 abstract "The paper contains the construction of a general theory of Boolean-valued algebras: There are introduced the notions of a homeomorphism, congruence, subalgebra and direct product. It is shown that these algebras possess properties that are totally analogous to the properties of two-valued algebras. To every Boolean-valued algebra there is related a certain universal algebra , called the normal extension of , whose elements are all the partitions of unity of the given Boolean algebra, with naturally extended operations. The equational equivalence of an arbitrary Boolean-valued algebra and its normal extension is proved. It is shown that every homomorphism of a Boolean-valued algebra can be uniquely extended to a homomorphism of its normal extension.Bibliography: 10 items." @default.
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- W2116785398 date "1973-04-30" @default.
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- W2116785398 title "BOOLEAN-VALUED ALGEBRAS" @default.
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- W2116785398 doi "https://doi.org/10.1070/sm1973v021n04abeh002938" @default.
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