Theory (mathematical logic)

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In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language.

Usually a deductive system is understood from context.

An element ϕ ∈ T of a theory T is then called an axiom of the theory, and any sentence that follows from the axioms ( T ⊢ ϕ is called a theorem of the theory.

Every axiom is also a theorem.

A first-order theory is a set of first-order sentences.

See also

External links