Definition:Theorem/Formal System

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Definition

Let $\mathcal L$ be a formal language.

Let $\mathscr P$ be a proof system for $\mathcal L$.


A theorem of $\mathscr P$ is a well-formed formula of $\mathcal L$ which can be deduced from the axioms and axiom schemata of $\mathscr P$ by means of its rules of inference.

That a WFF $\phi$ is a theorem of $\mathscr P$ may be denoted as:

$\vdash_{\mathscr P} \phi$


Also known as

A theorem $\phi$ of $\mathscr P$ is also called provable from $\mathscr P$.


Also see


Sources