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11 votes
0 answers
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Can every "not-too-big" differential field be thought of as actually consisting of functions?

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 $g(x)$ ...
Noah Schweber's user avatar
6 votes
0 answers
867 views

How to extend Ritt's theorem on elementary invertible bijective elementary functions?

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, ...
IV_'s user avatar
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3 votes
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97 views

Can the differential field of d.c.e. reals be nicely construed as a field of functions?

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 ...
Noah Schweber's user avatar