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14 votes
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Ordinal-valued sheaves as internal ordinals

Let $X$ be a topological space (feel free to add some separation axioms like “completely regular” if they help in answering the questions). Let $\alpha$ be an ordinal, identified as usual with $\{\...
Gro-Tsen's user avatar
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7 votes
0 answers
386 views

Sheafs in O-minimal Structures

Let $\mathcal{N} = (N, <, \ldots)$ be an o-minimal structure and let $X \subset N^m$ be a definable set. Following the procedure stablished by Edmundo, Jones and Peatfield in "Sheaf cohomology in o-...
Jonas Gomes's user avatar
5 votes
0 answers
146 views

Do presheaf toposes satisfy the full fan theorem?

Presheaf toposes satisfy LPO and (edit: if over categories with binary products) PAx and countable choice internally, so they automatically satisfy the stable fan theorem (every bar which is the ...
saolof's user avatar
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2 votes
0 answers
266 views

Relationship between coherent toposes/coherent logic and coherent sheaves

I've heard it claimed that the adjective "coherent" in logic/topos theory (i.e. coherent logic, coherent toposes, coherent categories) was adopted to fit in with the terminology of coherent sheaves in ...
dorebell's user avatar
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