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Page 66, Set Theory of - Herbert B. Enderton, Elements of Set Theory.

It says "but the class of all inductive sets is not a set."

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  • $\begingroup$ @MauroALLEGRANZA If $\omega$ does not exist, then the class of all inductive sets is a set. It is the empty set. I think the OP is working in $\text{ZFC}$ (in particular with the infinity axiom) and he or she wants to see that in this setting this class is not a set. This is more along the line of tetori's interpretation. $\endgroup$ – William Apr 23 '14 at 9:24
  • $\begingroup$ @William - you are right. $\endgroup$ – Mauro ALLEGRANZA Apr 23 '14 at 10:13
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Every limit ordinal is inductive, and the class of all limit ordinals is not a set. However if the class of all inductive set is a set, then the class of all limit ordinals is also a set, a contradiction.

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