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dc.contributor.author Detgen, Jonathan G.
dc.date.accessioned 2011-01-12T21:29:14Z
dc.date.available 2011-01-12T21:29:14Z
dc.date.issued 2010-12
dc.identifier.uri http://hdl.handle.net/10139/3018
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_US
dc.language.iso en_US en_US
dc.rights All rights reserved to author and California State University Channel Islands
dc.subject Mathematics thesis en_US
dc.subject Set theory en_US
dc.subject Powerset en_US
dc.subject Construction en_US
dc.subject Mathematics en_US
dc.title Constructible Families of Subsets, and Their Properties en_US
dc.type Thesis en_US

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