Stable Groups and Expansions of (z,+, 0)
نویسنده
چکیده
We show that if G is a stable group of finite weight with no infinite, infinite-index, chains of definable subgroups, then G is superstable of finite U rank. Combined with recent work of Palaćın and Sklinos, we conclude that (Z,+, 0) has no proper stable expansions of finite weight. A corollary of this result is that if P ⊆ Zn is definable in a finite dp-rank expansion of (Z,+, 0), and (Z,+, 0, P ) is stable, then P is definable in (Z,+, 0). In particular, this answers a question of Marker on stable expansions of the group of integers by sets definable in Presburger arithmetic.
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