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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

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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

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