 Hilbertian field (source code)

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= Hilbertian field
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= Hilbertian
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A <field> $K$ is Hilbertian if each finite family of <polynomials> irreducible over $K(T)$ and separable in its root variable remains irreducible of the same degree at infinitely many $T=a\in K$, after any finitely many prescribed bad parameter values are excluded. Equivalently, every finite separable extension of $K(T)$ has infinitely many unramified $K$-rational places whose residue extension retains its full degree.

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