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goblin GONE
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Good set theory in which to study ordinal-indexed sequences?

I'd like to "model" the absolute complement of a set $X$ as the ordinal-indexed sequence $\beta \mapsto V_\beta \setminus X$ where $V_\beta$ is the $\beta$ stage of the cumulative hierarchy. My understanding is that ZFC doesn't support ordinal-indexed sequences, so my question is, what is a good set theory in which to study this concept?

goblin GONE
  • 3.8k
  • 18
  • 39