View source for Theory (mathematical logic)

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 ==

* [[Axiomatic system]]
* [[Deductive system]]
* [[Formal system]]
* [[List of first-order theories]]

== External links ==

* [https://en.wikipedia.org/wiki/Theory_(mathematical_logic) Theory (mathematical logic)] @ Wikipedia.org 

[[Category:Logic]]
[[Category:Mathematics]]