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

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.

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.

Received:
Accepted:
Published online:
DOI: https://doi.org/10.5802/afst.1337
Timothy Mellor 1; Marcus Tressl 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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     title = {Non-axiomatizability of real spectra in $\mathcal{L}_\infty \lambda $},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {343--358},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
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Timothy Mellor; Marcus Tressl. Non-axiomatizability of real spectra in $\mathcal{L}_\infty \lambda $. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 21 (2012) no. 2, pp. 343-358. doi : 10.5802/afst.1337. https://afst.centre-mersenne.org/articles/10.5802/afst.1337/

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