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Non-axiomatizability of real spectra in 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 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.

On a non-vanishing Ext

Laszlo Fuchs, Saharon Shelah (2003)

Rendiconti del Seminario Matematico della Università di Padova

Separable k -free modules with almost trivial dual

Daniel Herden, Héctor Gabriel Salazar Pedroza (2016)

Commentationes Mathematicae Universitatis Carolinae

An R -module M has an almost trivial dual if there are no epimorphisms from M to the free R -module of countable infinite rank R ( ω ) . For every natural number k > 1 , we construct arbitrarily large separable k -free R -modules with almost trivial dual by means of Shelah’s Easy Black Box, which is a combinatorial principle provable in ZFC.

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