On Some Min-Max Cardinals on Boolean Algebras

This thesis is concerned with cardinal functions on Boolean Algebras (BAs) in general, and especially with min-max type functions on atomless BAs. The thesis is in two parts: (1) We make use of a forcing technique for extending Boolean algebras. elsewhere. Using and modifying a lemma of Koszmider, and using CH, we prove some general extension lemmas, and in particular obtain an atomless BA, A such that f(A) = smm(A) = w \u3c u(A) = w1. (2) We investigate cardinal functions of min-max and max type and also spectrum functions on moderate products of Boolean algebras. We prove several theorems determining the value of a function on a moderate product in terms of the values of that function on the factors