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 is a formal system used in mathematics, philosophy, linguistics, and computer science.
Propositional calculus (also called propositional logic, sentential calculus, or sentential logic) is the branch of mathematical logic concerned with the study of propositions (whether they are true or false) that are formed by other propositions with the use of logical connectives, and how their value depends on the truth value of their components.
In logic, quantification is a construct that specifies the quantity of specimens in the domain of discourse that satisfy an open formula.
In elementary mathematics, a variable is an alphabetic character representing a number, called the value of the variable, which is either arbitrary or not fully specified or unknown.