Without success, I have been trying to find who was the first to prove the folklore result that any finite support iteration of non-trivial posets adds Cohen reals at limits steps. Does anybody know?
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1$\begingroup$ But isn't this very easy once you understand the basic notions? $\endgroup$– Joel David HamkinsCommented May 31 at 1:18
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1$\begingroup$ The idea is that, if you fix a (name for a) nontrivial condition $\dot p_n$ at stage $n$, then any dense set for Cohen-real forcing translates into a dense set of conditions in the forcing iteration, namely, the condition that exhibit the corresponding relation to these fixed $\dot p_n$. So the iteration generic will add a Cohen real by considering how it relates to those conditions. $\endgroup$– Joel David HamkinsCommented May 31 at 1:30
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$\begingroup$ @JoelDavidHamkins I'm not asking about the proof, but I want to know who this result is due to, or where it was proved the first time. I'm asking about the history. $\endgroup$– dragoonCommented May 31 at 4:15
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2$\begingroup$ Laver certainly understood this fact about finite support iterations when he wrote his paper on the Borel conjecture (1976). I just checked, though, and I can't see any hint in his paper of who first proved it. $\endgroup$– Will BrianCommented May 31 at 9:26
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$\begingroup$ Thank you @WillBrian for the information. $\endgroup$– dragoonCommented Jun 5 at 1:15
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