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\title{Birkhoff's Representation Theorem For Finite Distributive
  Lattices}

\author{Matthew Doty}

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\begin{abstract}
  This theory proves a theorem of Birkhoff that asserts that any
  finite distributive lattice is isomorphic to the set of
  \emph{down-sets} of that lattice's join-irreducible elements. The
  isomorphism preserves order, meets and joins as well as
  complementation in the case the lattice is a Boolean algebra. A
  consequence of this representation theorem is that every finite
  Boolean algebra is isomorphic to a powerset algebra.
\end{abstract}

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