Suppose we are considering first-order logic without equality without any relation symbols. Since there are no relation symbols, not even equality, does this mean that this language is empty?
2026-03-31 19:16:58.1774984618
Is bare first order logic without equality an empty language?
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Basically yes - if you additionally outlaw the nullary connectives $\top$ and $\perp$, then indeed there are no well-formed formulas in this system. (Of course if you include them then Daniel Schepler's comment applies.)