# Abstract Stationary logic was introduced by Barwise and Makkai (these Notices, 23, A-594). A back and forth criterion for elementary equivalence for $\mathrm{L}(\mathrm{aa})$ and $\mathrm{L}_{\infty\omega_1}(\mathrm{aa})$ is given. This can be used to prove Feferman-Vaught-type theorems for these logics and to disprove Beth's theorem for L(aa) using ideas of Shelah. We alo get the following Interpolation theorem: Let $\mathrm{K}_1, \mathrm{~K}_2$ be two disjoint PC-classes for L(aa) which are cloced under $\mathrm{L}_{{ }_{\infty} \omega_1}$ (aa)-elementary equivalence. Then they can be separated by an EC-class of $\mathrm{L}(\mathrm{aa})$. A similar Beth-definability theorem holds, too. $\mathrm{L}(\mathrm{aa})$ can al so be characterized as the strongest compact fragment of $\mathrm{L}_{\infty 0 \omega_1}$ (aa). (Received May 27, 1977.)