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Non-axiomatizability of real spectra in $ℒ_{\infty} λ$

Timothy Mellor; Marcus Tressl — 2012

Annales de la faculté des sciences de Toulouse Mathématiques

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 $ℒ_{\infty} λ$ 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.

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Non-axiomatizability of real spectra in ℒ ∞ λ

Non-axiomatizability of real spectra in $ℒ_{\infty} λ$