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This question is basically a special case of this older question of mine, which is still unanswered. Let $\mathcal{D}$ be the field of d.c.e. reals; these turn out to be exactly the reals $\alpha$ for ...

Previously asked and bountied at MSE without success: Let $\sim$ denote the "no-disagreement" relation between partial functions: $f\sim g$ iff there is no $x$ such that $f(x)$ and $g(x)$ ...

The elementary functions according to Liouville and Ritt are the functions of a complex variable built up by applying exponentiation, logarithms and/or algebraic operations finitely often. That means, ...

E.R. Kolchin has developed the differential Galois theory in 1950s. And it seems powerful a tool which can decide the solvability and the form of solutions to a given differential equation.(e.g. ...