Deligne's completeness theorem

In mathematics, Deligne's completeness theorem says a coherent topos has enough points. It was first introduced by Pierre Deligne in SGA 4.

In 1970s, the category theorist William Lawvere observed that Deligne's theorem implies the Gödel completeness theorem.

See also

• Barr's theorem

References

• M. Artin, A. Grothendieck, J. L. Verdier (eds.), Théorie des Topos et Cohomologie Etale des Schémas - SGA 4. II , LNM 270 Springer Heidelberg 1972.
• Benjamin Frot, Godel's Completeness Theorem and Deligne's Theorem, https://arxiv.org/abs/1309.0389
• Lawvere, F. W. (1975). "Continuously Variable Sets: Algebraic Geometry= Geometric Logic". Proc. Logic Colloquium Bristol 1973. Amsterdam: North-Holland. pp. 135–156.

Further reading

• "Deligne completeness theorem in nLab".