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An existence theorem for 1-atomic standard models of $L_{\omega \omega }(Q_1)$ (more weak than usual “atomic models”) and applications of $L_{\omega \omega }(Q_1)$ to $L_{\omega \omega }$ are the results of this note.

An existence theorem for 1-atomic standard models of $L_{\omega \omega }(Q_1)$ (more weak than usual “atomic models”) and applications of $L_{\omega \omega }(Q_1)$ to $L_{\omega \omega }$ are the results of this note.