Stark's conjectures and Hilbert's twelfth problem.

Roblot, Xavier-François

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Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under G extends to a linear order on X also invariant under G. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set X, there is a linear preorder ≤ on the powerset 𝓟X invariant under G and such that if A is a proper subset of B, then...