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A class of structures C is said to have the extension property for partial automorphisms (EPPA) if, whenever C1 and C2 are structures in C, C1 finite, C1 ⊆ C2, and p1, p2, . . . , pn are partial automorphisms of C1 extending to automorphisms of C2, then there exist a finite structure C3 in C and automorphisms α1, α2, . . . , αn of C3 extending the pi. We… (More)

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)

We study the groups GalL(T ) and GalKP (T ), and the associated equivalence relations EL and EKP , attached to a first order theory T . An example is given where EL 6= EKP (a non G-compact theory). It is proved that EKP is the composition of EL and the closure of EL. Other examples are given showing this is best possible.

- Daniel Lascar, Bruno Poizat
- J. Symb. Log.
- 1979

- Daniel Lascar
- J. Symb. Log.
- 1992

- Daniel Lascar, Anand Pillay
- J. Symb. Log.
- 2001

A hyperimaginary is an equivalence class of a type-definable equivalence relation on tuples of possibly infinite length. The notion was recently introduced in [?], mainly with reference to simple theories. It was pointed out there how hyperimaginaries still remain in a sense within the domain of first order logic. In this paper we are concerned with several… (More)

- Daniel Lascar
- J. Symb. Log.
- 1982

- Daniel Lascar
- Arch. Math. Log.
- 1991

- Chantal Berline, Daniel Lascar
- Ann. Pure Appl. Logic
- 1986

- Daniel Lascar, Anand Pillay
- J. Symb. Log.
- 1999