| 21. | Other uses of the axiom of choice are more subtle.
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| 22. | All these are linked in one way or another to the axiom of choice.
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| 23. | In 1964, model of NBG with global choice replaced by the axiom of choice.
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| 24. | If the axiom of choice is not assumed we need to do something different.
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| 25. | The proof requires either the axiom of choice or a weakened form of it.
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| 26. | The answer to that question involves the axiom of choice.
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| 27. | In the absence of the axiom of choice, the reverse implications are all unprovable.
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| 28. | As far as I can tell, you're interpreting the axiom of choice as saying
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| 29. | :: : : Using the axiom of choice is extremely ambitious in this context.
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| 30. | This requires a suitable version of the axiom of choice.
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