Every Boolean algebra is isomorphic to the Boolean algebra of sets. The theorem is equivalent to the maximal ideal theorem, which can be proved without using the axiom of choice (Mendelson 1997, p. 121).
Boolean Representation Theorem
See also
Boolean Algebra, Maximal Ideal TheoremExplore with Wolfram|Alpha
References
Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, p. 121, 1997.Stone, M. "The Representation Theorem for Boolean Algebras." Trans. Amer. Math. Soc. 40, 37-111, 1936.Referenced on Wolfram|Alpha
Boolean Representation TheoremCite this as:
Weisstein, Eric W. "Boolean Representation Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BooleanRepresentationTheorem.html