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We give a criterion involving existence of many generic sequences of automorphisms for a countable structure to have the small index property. We use it to show that (i) any ω-stable ω-categorical structure , and (ii) the random graph has the small index property. We also show that the automorphism group of such a structure is not the union of a countable… (More)
A class of structures C is said to have the extension property for partial automorphisms (EPPA) if, whenever C 1 and C 2 are structures in C, C 1 finite, C 1 ⊆ C 2 , and p 1 , p 2 ,. .. , pn are partial automorphisms of C 1 extending to automorphisms of C 2 , then there exist a finite structure C 3 in C and automorphisms α 1 , α 2 ,. .. , αn of C 3… (More)
The Canadian Penning Trap mass spectrometer has made mass measurements of 33 neutron-rich nuclides provided by the new Californium Rare Isotope Breeder Upgrade facility at Argonne National Laboratory. The studied region includes the 132Sn double shell closure and ranges in Z from In to Cs, with Sn isotopes measured out to A=135, and the typical measurement… (More)
We study the groups Gal L (T) and Gal KP (T), and the associated equivalence relations E L and E KP , attached to a first order theory T .