For every coherent theory T, every topological space X, and every continuous assignment of model-theoretic types p:X→ S(T), does there exist a sheaf model M of T over X such that, for every point x∈ X, the set-based fibre M_x realises the assigned type p(x)?

Kanalas' problem of continuously realising types

For every coherent theory $\mathcal{T}$ , every topological space $X$ , and every continuous assignment of model-theoretic types $p:X\to S(\mathcal{T})$ , does there exist a sheaf model $\mathcal{M}$ of $\mathcal{T}$ over $X$ such that, for every point $x\in X$ , the set-based fibre $\mathcal{M}_x$ realises the assigned type $p(x)$ ?

References

Primary source

arXiv

Additional references

A counterexample to Kanalas' problem of continuously realising types — arXiv

model-theory topos-theory

Posted 1 month ago

Progress summary

Refreshed 1 month ago

Claimed solved

An unrefereed preprint claims to have found a counterexample, but the result has not been independently confirmed.

Kanalas' problem asks whether continuously varying model-theoretic types can always be realised as fibres of a sheaf model. No proposer or original date is identified in the retrieved material.

August 2026 counterexample

A preprint reports an explicit counterexample to the proposed continuous realisation principle, giving a negative answer to Kanalas' problem. The claim is unrefereed and remains unverified.

Current status (as of August 2026): A preprint claims the principle is false, but the counterexample has not been independently verified.

Sources

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