Term

Last updated Nov 1, 2022

The Set $\mathcal{T}$ of $\mathcal{L}$-Terms is the smallest set such that the following properties hold:

1. $c \in \mathcal{T}$ for each $c \in \mathcal{C}$
2. ${v_{i} : i \in \mathbb{N}} \subset \mathcal{T}$, where each $v_{i}$ is a distinct Variable Symbol for each $i \in \mathbb{N}$.
3. If $t_{1}, \dots, t_{n_{f}} \in \mathcal{T}$, then $f(t_{1}, \dots, t_{n_{f}}) \in \mathcal{T}$.

1. Note that the 3rd property makes sense when we interpret it with a Language Structure, since the inputs to the Function are either
   1. A Constant Symbol
   2. A Variable Symbol
   3. The output of another Function.
2. Terms are finite strings. Thus, they can only include finitely many Variable Symbols.

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