Editing First-order logic (section)

====Terms====
The set of ''[[Term (logic)|terms]]'' is [[inductive definition|inductively defined]] by the following rules:<ref>G. Takeuti, 'Proof Theory' (1989, p.6)</ref>
# ''Variables''. Any variable symbol is a term.
# ''Functions''. If ''f'' is an ''n''-ary function symbol, and ''t''<sub>1</sub>, ..., ''t''<sub>''n''</sub> are terms, then ''f''(''t''<sub>1</sub>,...,''t''<sub>''n''</sub>) is a term. In particular, symbols denoting individual constants are nullary function symbols, and thus are terms.
Only expressions which can be obtained by finitely many applications of rules 1 and 2 are terms. For example, no expression involving a predicate symbol is a term.