Terms (Predicate Logic)

The $\sigma$-terms of a first-order language over $\sigma$ are the expressions from $A_{\sigma }^{\ast }$ defined via the following rules:

• every variable is a $\sigma$-term
• every constant in $\sigma$ is a $\sigma$-term
• if the expressions $t_1,...,t_n$ are $\sigma$-therms and $f$ is an $n$-ary function in $\sigma$, then the expression $f(t_1,...,t_n)$ is also a $\sigma$-term