A criterion of elementary equivalence of automorphism groups of reduced Abelian p-groups

A Criterion of Elementary Equivalence of Automorphism Groups of Unreduced Abelian p-Groups

“…Theorem 6 (Roizner [18]). Let A and A be some reduced Abelian p-groups with basic subgroups B and B , respectively, p ≥ 3.…”

“…Theorem 7 implies that either |G| = |B| or |B| < |G| ≤ 2 ω . The |B|-bounded second-order theory of the group G is expressed by the first-order language of Aut A in [18]. The second-order theory of the divisible part D is expressed in [9].…”