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Oct 10, 2013 at 5:47 vote accept Mohammad Golshani
May 18, 2011 at 12:20 comment added Joel David Hamkins Another issue is that you will need a GCH-type assumption in order even to know that individual factors $\text{Add}(\alpha^{++},1)$ do not collapse cardinals. After all, this partial order will force $2^{\alpha^+}=\alpha^{++}$, which will collapse cardinals unless this was true originally. If you start with GCH, then perhaps you may want to use Easton support, rather than countable support, and then things will be much better for you.
May 18, 2011 at 10:51 history answered Joel David Hamkins CC BY-SA 3.0