Theory (mathematical logic)

Set of sentences in a formal language

In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood from context, giving rise to a formal system that combines the language with deduction rules. An element ϕ ∈ T {\displaystyle \phi \in T} of a deductively closed theory T {\displaystyle T} is then called a theorem of the theory.

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