The proposition that every proper ideal of a Boolean algebra can be extended to a maximal ideal. It is equivalent to the Boolean representation theorem, which can be proved without using the axiom of choice (Mendelson 1997, p. 121).
Maximal Ideal Theorem
See also
Boolean Representation TheoremExplore with Wolfram|Alpha
References
Lós, J. "Sur la théorème de Gödel sur les theories indénombrables." Bull. de l'Acad. Polon. des Sci. 3, 319-320, 1954.Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, p. 121, 1997.Rasiowa, H. and Sikorski, R. "A Proof of the Completeness Theorem of Gödel." Fund. Math. 37, 193-200, 1951.Rasiowa, H. and Sikorski, R. "A Proof of the Skolem-Löwenheim Theorem." Fund. Math. 38, 230-232, 1952.Referenced on Wolfram|Alpha
Maximal Ideal TheoremCite this as:
Weisstein, Eric W. "Maximal Ideal Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MaximalIdealTheorem.html