Timeline for Which forcing types preserve the axiom of determinacy?

8 events

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Jun 15, 2020 at 7:27	history	edited	CommunityBot		Commonmark migration
Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Aug 25, 2014 at 17:36	history	edited	Asaf Karagila♦	CC BY-SA 3.0	deleted 8 characters in body
Aug 25, 2014 at 17:34	comment	added	Asaf Karagila♦		Alright then, your point is a good one. Let me rule that option out.
Aug 25, 2014 at 17:33	comment	added	Joel David Hamkins		But if you add only a set of sets of reals, but no reals and no set of reals, then of course AD is preserved, since it has to do with sets of reals and reals.
Aug 25, 2014 at 17:27	comment	added	Asaf Karagila♦		@Joel: Subset of $\mathcal P(\Bbb R)$. Since we can think of $\Bbb R$ as $\mathcal P(\omega)$, adding a real, a set of reals, or a set of sets of reals are all included in this definition. But both interpretations are interesting anyway. :-)
Aug 25, 2014 at 17:19	comment	added	Joel David Hamkins		Could you clarify: do you mean that $\mathbb{P}$ adds a subset of $\mathbb{R}$, or only that it adds a subset of ${\cal P}(\mathbb{R})$? (Your phrasing, "adds a subset to ${\cal P}(\mathbb{P})$" could be interpreted as adding an element to that power set, or as adding a subset to the power set.)
Aug 25, 2014 at 17:11	history	asked	Asaf Karagila♦	CC BY-SA 3.0