The sheaf representation of finitely presented Heyting algebras equals profinite completion algebraically, with the K-topos (ex/reg-completion of profinite Heyting algebras) generalizing uniform interpolation via its internal logic.
Flabby and injective objects in toposes
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Coexact completion of profinite Heyting algebras and uniform interpolation
The sheaf representation of finitely presented Heyting algebras equals profinite completion algebraically, with the K-topos (ex/reg-completion of profinite Heyting algebras) generalizing uniform interpolation via its internal logic.