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Is bounded-$\mathcal L_{\omega_1,\omega_1}$ significantly different from $\mathcal L_{\omega_1,\omega_1}$?
Take the language $\mathcal L(=,\in)_{\omega_1,\omega_1}$, if we restrict infinite quantification strings, i.e. of the forms $``(\forall v_i)_{i \in \omega}"; ``(\exists v_i)_{i \in \omega}"$, to ...
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