Nabla Algebras and Chu Spaces
Nabla Algebras and Chu Spaces
Nabla Algebras and Chu Spaces
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Foreword<br />
Basic observations<br />
∇-algebras<br />
Lifting constructions on <strong>Chu</strong> spaces<br />
Vietoris endofunctor on Stone spaces<br />
Semantic equivalences<br />
The following semantic equivalences hold:<br />
✸ϕ ≡ ∇{ϕ, ⊤}<br />
✷ϕ ≡ ∇∅ ∨ ∇{ϕ}<br />
So ✷ <strong>and</strong> ✸ can be defined in terms of ∇.<br />
Question: Can this equivalences be expressed also axiomatically?<br />
Desiderata<br />
Intrinsic, non roundabout axiomatization for ∇;<br />
Aless<strong>and</strong>ra Palmigiano (joint work with Yde Venema) <strong>Nabla</strong> <strong>Algebras</strong> <strong>and</strong> <strong>Chu</strong> <strong>Spaces</strong><br />
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