2 problems

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The Artin-gluing conjecture for replacing an open subtopos
Artin-gluing conjecture. The theory $\mathbb{T}+\mathbb{E}/\phi$ is classified by the topos
Conjectureopenartin-gluing geometric-logic topos-theoryarXiv posted 2 days ago
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Moerdijk's infinitary extension conjecture for geometric logic
Let $\Sigma$ be a signature, and let $\Sigma$ -structures in a Grothendieck topos $\mathcal E$ be the corresponding category of models. Moerdijk's conjecture concerns the result cha…
Conjectureopengeometric-logic infinitary-logic topos-theoryarXiv posted 2 days ago

The Artin-gluing conjecture for replacing an open subtopos