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Deductively closed

In mathematical logic, a set ⁠T{\displaystyle {\mathcal {T}}}⁠ of logical formulae is deductively closed if it contains every formula ⁠φ{\displaystyle \varphi }⁠ that can be logically deduced from ⁠T{\displaystyle {\mathcal {T}}}⁠; formally, if ⁠T⊢φ{\displaystyle {\mathcal {T}}\vdash \varphi }⁠ always implies ⁠φ∈T{\displaystyle \varphi \in {\mathcal {T}}}⁠.

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