@Misc{BSPACE.MIZ,
  AUTHOR = {Alama, Jesse},
   TITLE = {The Vector Space of Subsets of a Set Based on Disjoint Union},
     DAY = {9},
   MONTH = {October},
    YEAR = {2007},
ADDRESS1 = {Department of Philosophy\\Stanford University},
 SUMMARY = {For each set $X$, the power set of $X$ forms a
               vector space over the field $F_{2}$ (the two-element
               field $\{0,1\}$ with addition and multiplication
               done modulo $2$): vector addition is disjoint union,
               and scalar multiplication is defined by the two equations
               ($1 \cdot x := x$, $0 \cdot x := \emptyset$ for subsets
               $x$ of $X$).  See \cite{kelley}, Exercise 2.K, for
               more information.},
  section1 = {Preliminaries: Induction on Sequences of Elements
                  of a 1-sorted Structure},
  section2 = {The Two-element Field $F_{2}$},
  section3 = {Set-theoretical Preliminaries},
  section4 = {The Boolean Vector Space of Subsets of a Set},
  section5 = {The Linear Independence and Linear Span of Singleton Subsets}}

@Book{kelley,
  author = {Kelley, John L.},
  title = {General Topology},
  publisher = {Springer-Verlag},
  year = {1955},
  volume = {27},
  series = {Graduate Texts in Mathematics}}
