A structure theorem for differential algebras
Super real closed rings
A super real closed ring is a commutative ring equipped with the operation of all continuous functions ℝⁿ → ℝ. Examples are rings of continuous functions and super real fields attached to z-prime ideals in the sense of Dales and Woodin. We prove that super real closed rings which are fields are an elementary class of real closed fields which carry all o-minimal expansions of the real field in a natural way. The main part of the paper develops the commutative algebra of super real closed rings, by...
Non-axiomatizability of real spectra in
We show that the property of a spectral space, to be a spectral subspace of the real spectrum of a commutative ring, is not expressible in the infinitary first order language of its defining lattice. This generalises a result of Delzell and Madden which says that not every completely normal spectral space is a real spectrum.
An existence theorem for systems of implicit differential equations
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