Alphabet (Predicate Logic)

Given a vocabulary $\sigma$, the alphabet $A_{\sigma }$ of a first-order language over $\sigma$ is a set of symbols comprising:

• a countably infinite set of variables $\{x,y,z,...\}$ (with super and subscripts)
• $\top ,\perp$: the Boolean values true and false
• $\neg ,\wedge ,\vee ,\to ,\leftrightarrow$: the logical connectives
• $\forall ,\exists$: the quantifiers’ symbols
• $=$: the equality symbol; $t_1\ne t_2\text{ may replace }\neg (t_1=t_2)$
• $(,)$: the parentheses
• $,$: the comma
• all the constant, predicate, and function, symbols (with their associated arity) from $\sigma$