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Asaf Karagila ♦
Asaf Karagila ♦
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I've heard from others about the WO($\kappa$) as a counterpart of AC($\kappa$), but I cannot find a suitable way to express it in ZF since "every set of cardnality $\kappa$ can be well-ordered" is meaningless. Does WO($\kappa$) really exist?

I've found one. "Every set in $V_\kappa$ can be well-ordered." Is this right?

I've heard from others about the WO($\kappa$) as a counterpart of AC($\kappa$), but I cannot find a suitable way to express it in ZF since "every set of cardnality $\kappa$ can be well-ordered" is meaningless. Does WO($\kappa$) really exist?

I've heard from others about the WO($\kappa$) as a counterpart of AC($\kappa$), but I cannot find a suitable way to express it in ZF since "every set of cardnality $\kappa$ can be well-ordered" is meaningless. Does WO($\kappa$) really exist?

I've found one. "Every set in $V_\kappa$ can be well-ordered." Is this right?

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Well-Ordering theorem of cardinal$\kappa$

I've heard from others about the WO($\kappa$) as a counterpart of AC($\kappa$), but I cannot find a suitable way to express it in ZF since "every set of cardnality $\kappa$ can be well-ordered" is meaningless. Does WO($\kappa$) really exist?