Date of Award
Doctor of Philosophy (PhD)
James D. Monk
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 < 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.
Selker, Kevin, "On Some Min-Max Cardinals on Boolean Algebras" (2015). Mathematics Graduate Theses & Dissertations. 34.