Definition:First Order Logic with Identity

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Definition

A system of first order logic with identity is a system of predicate logic with the following elements in its alphabet:

Connectives

   \(\displaystyle \land \)   \(\displaystyle : \)   the conjunction sign             
   \(\displaystyle \lor \)   \(\displaystyle : \)   the disjunction sign             
   \(\displaystyle \implies \)   \(\displaystyle : \)   the conditional sign             
   \(\displaystyle \iff \)   \(\displaystyle : \)   the biconditional sign             
   \(\displaystyle \neg \)   \(\displaystyle : \)   the negation sign             


Quantifiers

   \(\displaystyle \exists \)   \(\displaystyle : \)   the existential quantifier sign             
   \(\displaystyle \forall \)   \(\displaystyle : \)   the universal quantifier sign             


Identity

   \(\displaystyle = \)   \(\displaystyle : \)   the equality sign             


Sources