| 11. | Hence this statement is strictly weaker than the axiom of choice.
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| 12. | This follows from Zorn's lemma, an equivalent formulation of the Axiom of Choice.
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| 13. | If the axiom of choice holds, every cardinal number has an initial ordinal.
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| 14. | For example, the MIT for rings implies the axiom of choice.
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| 15. | Thus the axiom of choice is not generally available in constructive set theory.
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| 16. | This theorem does not rely on the axiom of choice.
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| 17. | The status of the axiom of choice varies between different varieties of constructive mathematics.
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| 18. | The well-ordering principle is equivalent to the axiom of choice.
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| 19. | This second definition makes sense without the axiom of choice.
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| 20. | He continues to be involved with Axiom of Choice and with the Dastan ensemble.
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