Timeline for Forcing as a new chapter of Galois Theory?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 30, 2012 at 19:38 | comment | added | Mirco A. Mannucci | @Asaf: I apologize for not replying (yet) to the many answers and comments on this question. My only excuse is: I was simply overwhelmed, and needed time to process the data. Rest assured, though, That I will reply to all, when digestion is complete. | |
| Jun 28, 2012 at 17:05 | comment | added | Asaf Karagila♦ | @Downvoter: I enjoyed the downvote, thanks! I hope you at least bothered to read the answer... | |
| Jun 24, 2012 at 23:39 | comment | added | David Roberts♦ | "does not have any non-trivial automorphism" what in this case is an automorphism? Given that the OP mentioned a structural viewpoint, one could imagine that a self-equivalence of the category of sets in the extension fixing the sets in the base up to isomorphism might be a more appropriate automorphism than what is usually used in (material) set theory. | |
| Jun 24, 2012 at 9:58 | comment | added | Stefan Geschke | Andres points at something important that hasn't been stressed enough in this discussion, I think. A transitive model of set theory does not have any non-trivial automorphism. Hence the literal Galois group of a forcing extension is always trivial and in order to come up with an interesting theory it is necessary to look stabilizers of names and so on, as pointed out above. | |
| Jun 24, 2012 at 5:53 | comment | added | Andrés E. Caicedo | "generic extensions of the same forcing need not be isomorphic." They cannot be isomorphic, unless they are equal. (By Mostowski's collapsing theorem.) | |
| Jun 24, 2012 at 5:44 | history | answered | Asaf Karagila♦ | CC BY-SA 3.0 |