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Sep 17, 2020 at 4:07 comment added jonasreitz @MircoA.Mannucci - just responded - great question!
Sep 13, 2020 at 18:46 comment added Mirco A. Mannucci @jonasreitz when u have a chance, take a look at my new "geological" question. Perhaps you have something to contribute there too. All the best, Mirco
Sep 4, 2020 at 13:38 vote accept Mirco A. Mannucci
Sep 1, 2020 at 20:54 comment added Mirco A. Mannucci @jonasreitz my answer to your answer is in the ADDENDUM. Hopefully there will be more "digging", just to remain on geology...
Sep 1, 2020 at 7:52 comment added Asaf Karagila arxiv.org/abs/2006.04514, Yes, adding a Cohen real to L has a proper class of grounds. However their intersection is L. More interestingly, their union is a ZF model which is not a ground of the Cohen extension.
Sep 1, 2020 at 4:28 comment added none Will there generally be a proper class of A-grounds and is it ok to intersect them all in that case?
Sep 1, 2020 at 3:25 comment added jonasreitz @AsafKaragila - I must admit, questions about forcing without AC seem like a terrible quagmire to me - but that just says I need to work more with models without choice! Did I read your comment correctly - adding a Cohen real can add class-many grounds?
Sep 1, 2020 at 3:21 comment added jonasreitz Thanks, @MircoA.Mannucci - this is something like my interest in this question as well. The introduction to your question above pointed me in the direction of Timothy Chow's two recent questions about forcing - thank you, they were great reads and your answers were as well.
Aug 31, 2020 at 21:31 comment added Asaf Karagila Removing AC from the equation is so much more interesting. Especially in the case of a Cohen real, where adding the one set will invariably add a lot of grounds (and over $L$ and other "small models" a proper class of them).
Aug 31, 2020 at 19:33 history edited jonasreitz CC BY-SA 4.0
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Aug 31, 2020 at 17:43 comment added Mirco A. Mannucci Jonas, I have no time to read your answer now (but I will!). You already got my like for 1) taking the first stab 2) because I "smelled " your answer and it is definitely going where I would like it to go. Detailed comments forthcoming . Meanwhile I can tell you the REAL reason motivating my question (Siths never tell you their real agenda, but I suspect that Andreas had already understood, his is simply too good to fool ). My question is there because i want to really understand forcing, and by that I mean really really really. So I am trying first to understand its opposite :)
Aug 31, 2020 at 15:52 history answered jonasreitz CC BY-SA 4.0