AN INTRODUCTION TO BOOLEAN ALGEBRAS

<p>This thesis discusses the topic of Boolean algebras. In order to build intuitive understanding of the topic, research began with the investigation of Boolean algebras in the area of Abstract Algebra. The content of this initial research used a particular notation. The ideas of partially ordered sets, lattices, least upper bounds, and greatest lower bounds were used to define the structure of a Boolean algebra. From this fundamental understanding, we were able to study atoms, Boolean algebra isomorphisms, and Stone’s Representation Theorem for finite Boolean algebras. We also verified and proved many properties involving Boolean algebras and related structures.</p> <p>We then expanded our study to more thoroughly developed theory. This comprehensive theory was more abstract and required the use of a different, more universal, notation. We continued examining least upper and greatest lower bounds but extended our knowledge to subalgebras and families of subsets. The notions of cardinality, cellularity, and pairwise disjoint families were investigated, defined, and then used to understand the Erdös-Tarski Theorem.</p> <p>Lastly, this study concluded with the investigation of denseness and incomparability as well as normal forms and the completion of Boolean algebras.</p>

Name thesis:degree_name

Master of Arts in Mathematics

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2016

Author dc:creator

• Schardijn, Amy

Contributors dc:contributor

• Llosent, Giovanna

• boolean
• algebras
• set theory
• boole
• lattice
• ultrafilter
• Algebra

Repository record dc:identifier

https://scholarworks.lib.csusb.edu/etd/421

OAI identifier oai:identifier

oai:scholarworks.lib.csusb.edu:etd-1477