Real Algebraic and Analytic Geometry

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319. Timothy Mellor, Marcus Tressl:
Non-axiomatizability of real spectra in L∞λ.

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Submission: 2011, January 23.

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 L∞λ 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.

Mathematics Subject Classification (2010): 14P10, Secondary: 03C64, 03C75.

Keywords and Phrases: spectral spaces, real spectrum, model theory.

Full text, 11p.: dvi 70k, pdf 362k.

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