2:30-3:30 pm

Room 3307, CUNY Graduate Center

365 Fifth Avenue at 34th Street

**September 4:** Alexei Mishchenko (Omsk University), *Universal invariants for classes of abelian groups*

**Abstract: ** The problem of elementary equivalence for abelian groups was solved by W. Szmielew in 1955. She introduced a criterion of elementary equivalence of two abelian groups in terms of elementary invariants. We define universal invariants for arbitrary class of abelian groups and prove analogues of Szmielew's theorem for universal classes of abelian groups. We introduce the concept of the principal universal class as a universal class generated by a group A. For each principal universal class we introduce a canonical group so that the two principal universal classes are equal if and only if they have the same canonical group.

**October 2:** Anna Choromanska (NYU), *TBA*

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