Is it possible to construct in the signature without equality the formula, which has 2-elements model and hasn't 3-elements model?
I think no, but have no idea how to prove it.
2026-03-25 14:21:59.1774448519
Signature without equality
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Recall that for any formulas without equality the following holds.
So, if your formula without equality has any model whatsoever, it has a countable model.