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Jan 23, 2022 at 9:22 comment added Zuhair Al-Johar @AndreasBlass, Agreed! Thanks for the correction. I've edited the question.
Jan 23, 2022 at 9:21 history edited Zuhair Al-Johar CC BY-SA 4.0
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Jan 23, 2022 at 9:16 vote accept Zuhair Al-Johar
Jan 23, 2022 at 6:27 history became hot network question
Jan 23, 2022 at 4:53 comment added Andreas Blass The question twice mentions "formula" (once with the constraint that $W$ isn't free) and twice mentions "sentence(s)". I assume (and Monroe Eskew and Ali Enayat apparently also assumed) that you mean "sentence", because the version with "formula fails --- the formula $(\exists y)\ y=x$ would be a counterexample.
Jan 23, 2022 at 4:38 answer added Ali Enayat timeline score: 18
Jan 22, 2022 at 22:40 comment added Monroe Eskew Yes, this follows from the reflection theorem and Lowenheim-Skolem.
Jan 22, 2022 at 22:27 history asked Zuhair Al-Johar CC BY-SA 4.0