Non-axiomatizability of real spectra in λ
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 21 (2012) no. 2, pp. 343-358.

Nous montrons que la propriété d’un espace spectral d’être un sous-espace spectral du spectre réel d’un anneau commutatif n’est pas exprimable dans le langage infinitaire du premier ordre λ de son treillis de définition. Ceci généralise un résultat de Delzell et Madden qui dit qu’en général, un espace spectral complètement normal n’est pas un spectre réel.

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 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.

DOI : 10.5802/afst.1337
Mellor, Timothy 1 ; Tressl, Marcus 2

1 Universität Regensburg, NWF I - Mathematik, D-93040 Regensburg, Germany
2 The University of Manchester, School of Mathematics, Oxford Road, Manchester M13 9PL, UK
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Mellor, Timothy; Tressl, Marcus. Non-axiomatizability of real spectra in $\mathcal{L}_\infty \lambda $. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 21 (2012) no. 2, pp. 343-358. doi : 10.5802/afst.1337. http://www.numdam.org/articles/10.5802/afst.1337/

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