The Structure of a Boolean Algebra Page: 1
iv, 56 leaves: ill.View a full description of this thesis.
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CHAPTER I
FUNDAMENTAL POSTULATES AND THEOREMS
Let ^ be a set. The purpose of this chapter is to
develop a form of a "free" Boolean algebra with as a
base, by imposing the usual Boolean operations on the set
H and thus generating new elements freely within explicitly
prescribed restrictions.
To this end let it be postulated that there exist a
set P containing Z as a subset, two binary operations
fl and U, and a unary operation 1, all closed on 21^
and a relation < on £1^ subject only to the following
restrictions:
Postulate 1.1, If A is an element of then A < A.
Postulate 1.2. If A, B, and C are elements of ^
and if A < B and B < C, then A < C.
Postulate 1.3. If A and B are elements of ]L^, and if
A < B and B < A, then A ~ B.
Postulate 1.4. If A, B, and C are elements of
then AO(BUC) < (A O B) U (A H C).
Postulate 1.5. If A, B, and C are elements of £3,
then A < (B D 0) if and only if A < B and A < 0.
Postulate 1.6. If A, B, and C are elements of
then (AUB) <C if and only if A <C and B <C.
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Bryant, June Anne. The Structure of a Boolean Algebra, thesis, August 1965; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc130610/m1/5/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .