Complete Boolean Algebra - Properties of Complete Boolean Algebras

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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