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Jul 7, 2016 at 16:17 comment added Tim Campion In the opposite of the direction you're interested in, note that Boney's result has been improved slightly by Brooke-Taylor and Rosicky. See these slides, which I believe refer to this paper.
Nov 28, 2015 at 18:26 answer added Rami Grossberg timeline score: 3
Nov 26, 2015 at 16:53 comment added user82740 @MohammadGolshani (+1) Very nice references. Thanks a lot!
Nov 26, 2015 at 8:59 comment added Mohammad Golshani See LARGE CARDINAL AXIOMS FROM TAMENESS IN AECS. In this paper it is shown that to get tameness, some large cardinal assumptions are needed. Of course it does not imply if we need large cardinals for Shelah's conjecture. On the other hand Vasey has proved Shelah's conjecture for universal classes without the use of any large cardinals. See Shelah's eventual categoricity conjecture in universal classes.
Nov 25, 2015 at 18:51 history asked user82740 CC BY-SA 3.0