Abstract:
Abstract: A subset X of a BA is independent if for any two finite
disjoint subsets F and G of X, the product of all members of F times
the product of the negatives of all members of G is nonzero. Given
an infinite BA A, we can consider Spind(A) = the set of all cardinalities
of maximal independent subset of A. Big question: when can a set
of infinite cardinals be the set Spind(A) of some BA? Answer: no
restrictions. The proof involves some simple constructions and some
elementary infinite combinatorics.
Beyond this main result we give some incomplete results
concerning
what happens to this spectrum of maximal independent subsets under
common algebraic operations.