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math.LO2026
Compact-Open Dualities for Stably Continuous Posets
Jérémie Marquès
We organize and generalize several dualities involving continuous posets. The main theorem reads $\mathbf{St}_α\mathbf{Inf}_{α'}\mathbf{Cont}_{β'}\mathbf{Sup}_β\simeq (\mathbf{St}_…
math.LO2026
The Constant Domain Axiom in Toposes
Jérémie Marquès
Constant domain intuitionistic logic admits a complete semantics in presheaf toposes, by interpreting sorts as constant presheaves and predicates as arbitrary sub-presheaves. The g…