Math 2.0

Concept

Deductive closure

Summary

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

Further reading

  1. Wikipedia, page 7750539, revision 1302527093, Deductive closure. adopted
About this page
TagCT4FZ84V45
URIm2://CT4FZ84V45
Aliasesclosure-logic, deductive-closure-principle, deductively-closed, deductively-closed-theory, deductively-defined-theory
Kindconcept
WritingW1 stated
Same as
Changed4 November 2026

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