Timeline for Logical endofunctors of Set?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Sep 29, 2010 at 13:26 | comment | added | Andreas Blass | Strictly speaking, Joel is correct that I proved the result he cites, but it was proved earlier by Vera Trnkova (Comm. Math. Univ. Carolinae 12 (1971) 227-233). My paper on this (Pac. J. Math. 63 (1976) 335-346) was followed by a correction about this point (Pac. J. Math 73 (1977) 540). | |
| Dec 9, 2009 at 1:36 | history | edited | Joel David Hamkins |
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| Nov 19, 2009 at 20:24 | answer | added | Joel David Hamkins | timeline score: 9 | |
| Nov 16, 2009 at 4:16 | comment | added | Mike Shulman | Here is a comment I learned from Nate Ackermann. Blass shows that any exact endofunctor of Set is a directed union of ultrapowers by countably-complete ultrafilters. Suppose our functor were just a single countably-complete ultrapower. Then it would also give an elementary embedding j: V → M for some transitive model M ⊆ V containing all the ordinals. But if j also preserves powersets, then M must also contain all the subsets of the ordinals, which implies it is all of V. Hence no single ultrapower can be a logical functor. | |
| Nov 4, 2009 at 3:25 | history | asked | Mike Shulman | CC BY-SA 2.5 |