TOPICS
Search

Maximal Ideal Theorem


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).


See also

Boolean Representation Theorem

Explore with Wolfram|Alpha

WolframAlpha

More things to try:

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 Theorem

Cite this as:

Weisstein, Eric W. "Maximal Ideal Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MaximalIdealTheorem.html

Subject classifications