In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model.
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete.
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
Propositional calculus is a branch of logic.
In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.