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Jun 8, 2023 at 16:51 vote accept Zuhair Al-Johar
Jun 8, 2023 at 16:50 comment added Zuhair Al-Johar So the usual upward Löwenheim–Skolem theorem fails drastically here. This is similar to the situation of characterizing the standard model of arithmetic in $\mathcal L_{\omega_1, \omega}$, where all models are countable! Thanks a lot.
Jun 8, 2023 at 11:07 history answered Joel David Hamkins CC BY-SA 4.0