Date of Award

Spring 1-1-2015

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

James D. Monk

Second Advisor

Keith Kearnes

Third Advisor

Agnes Szendrei

Fourth Advisor

Carol Cleland

Fifth Advisor

Natasha Dobrinen

Abstract

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.

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