The small index property and recursively saturated models of Peano arithmetic

Abstract

Abstract The small index property has been proved for several countable structures. See Hodges (1989) and Hodges et al. (1993) for more details. There exist countable ‘.N0-categorical structures which fail to have it (Lascar, 1991), see also p. 52 in this volume. Surprisingly, the case of uncountable saturated structures is easier, and it has been proved by Lascar and Shelah (1993) with the help of GCH. The question of the small index property is closely related to the possibility of recovering a structure from its automorphism group, and in the case of the recursively saturated model of Peano arithmetic, it has been raised by Kaye, Kossak and Kotlarski (Kaye et al., 1991).