Date of Award

Spring 1-1-2012

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

J. Donald Monk

Second Advisor

Keith A. Kearnes

Third Advisor

Agnes E. Szendrei

Abstract

This dissertation introduces a generalization of the cardinal invariant independence for Boolean algebras, suggested by the proof of the Balcar-Franek Theorem. The objects of study are independent sets of partitions under this new notion of independence. Generalizations of several known results regarding large and small independence are formulated and proved, and counterexamples provided for others. Notably the Balcar-Franek theorem itself is generalized.

Included in

Mathematics Commons

Share

COinS