Show simple item record

dc.contributor.author Detgen, Jonathan G. en
dc.date.accessioned 2011-01-12T21:29:14Z en
dc.date.available 2011-01-12T21:29:14Z en
dc.date.issued 2010-12 en
dc.identifier.uri http://hdl.handle.net/10139/3018 en
dc.description.abstract The focus of this paper is to find properties inherent to constructible families of subsets. From a family of subsets U = {A1,A2,...}, U1 is defined to be U∪ {(Ai)c,Am ∪ An,Am ∩ An : Ai,Am,An ∈ U}. From U1, U2 can be defined as U1 ∪{(Ai)c,Am ∪ An,Am ∩ An : Ai,Am,An ∈U1}. Whether these constructible families can be expanded infinitely or if they terminate at a greatest constructible family for a starting U, certain properties hold in general, and will be proven in this paper. Additionally, this paper will prove that the minimum requirements for a family U to construct the powerset P(X)of a given finite universe X of order n arethatallelements inXbepairwiseseparable in U and that U is a family of order i = dlog2 ne. Further study on constructible families of subsets includes construction of the powerset for infinite sets X, as well as going in the opposite direction of construction. Initial work in these areas is presented. Lastly, potential areas for application of constructible families are discussed. en
dc.language.iso en_US en
dc.rights All rights reserved to author and California State University Channel Islands en
dc.subject Mathematics thesis en
dc.subject Set theory en
dc.subject Powerset en
dc.subject Construction en
dc.subject Mathematics en
dc.title Constructible Families of Subsets, and Their Properties en
dc.type Thesis en

Files in this item


This item appears in the following Collection(s)

Show simple item record

Search DSpace

My Account

RSS Feeds