Properties of Complete Boolean Algebras
- Sikorski's extension theorem states that
if A is a subalgebra of a Boolean algebra B, then any homomorphism from A to a complete Boolean algebra C can be extended to a morphism from B to C.
- Every subset of a complete Boolean algebra has a supremum, by definition; it follows that every subset also has an infimum (greatest lower bound).
- For a complete boolean algebra both infinite distributive laws hold.
- For a complete boolean algebra infinite de-Morgan's laws hold.
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