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Monroe Eskew
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large ccc forcing that preserves CH

Can you name a ccc forcing with the following properties?

  1. Atomless

  2. The least size of a dense set is large, say at least $\aleph_3$, hopefully as big as you like.

  3. Existence is consistent with CH.

  4. Preserves CH.

If you can think of any, please list as many as you can.

Monroe Eskew
  • 18.6k
  • 5
  • 53
  • 114