Definition: Syntax of \(L\)
Given the sets \(C\), \(K\), \(V\), \(Q\) for constants, connectives, variables, and quantifiers, respectively, the language \(L\) is defined as follows:
- \(C\cup K\cup V \subseteq L\)
- If \(\pi_{\smtyp{\alpha}{\beta}} \in L\) and \(\sigma_{\alpha} \in L\), then \((\pi\sigma)_{\beta} \in L\).
- If \(\kappa \in \{\forall,\exists\}\), \(\chi \in V\) and \(\tau_{t} \in L\), then \((\kappa \chi \tau)_{t} \in L\)
- Nothing else is in \(L\).