[[Logic MOC]]
# Formal theory

A **formal theory** $\mathcal{T}$ in a [[Formal language]] $\mathcal{L}$ is a set of distinguished formulae $\mathcal{T} \sube \mathcal{L}$, #m/def/logic 
which are typically interpreted as formulae which are _true_ according to the theory and called **theorems** of the theory.
There are two usual routes to constructing such a theory

1. **Systematic** — $\mathcal{T}$ consists of all theorems of a given [[formal system]] in $\mathcal{L}$
2. **Semantic** — $\mathcal{T}$ consists of formulae which are true of a given [[model]] or interpretation of $\mathcal{L}$


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#state/develop | #lang/en | #SemBr