LYCOS RETRIEVER 
First-Order Logic: Cases
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If equality is considered to be a part of first order logic, then the equality symbol behaves syntactically as a binary predicate. This case is sometimes called first order logic with equality.
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Typed first-order logic allows variables and terms to have various [T]ypes (or sorts). If there are only a finite number of types, this does not really differ much from first-order logic, because one can describe the types with a finite number of unary predicates and a few axioms. Sometimes there is a special type Ω of truth values, in which case formulas are just terms of type Ω.
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(Note that in the Axiom of Comprehension, can be replaced by any formula expressible in first-order logic that contains as a free variable. Also note that may ... contain additional free variables , in which case the instance of the axiom schema must be prefixed by universal quantifiers .)
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