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More on the Ehrenfeucht-Fraisse game of length ω₁

Tapani Hyttinen, Saharon Shelah, Jouko Vaananen (2002)

Fundamenta Mathematicae

By results of [9] there are models and for which the Ehrenfeucht-Fraïssé game of length ω₁, E F G ω ( , ) , is non-determined, but it is consistent relative to the consistency of a measurable cardinal that no such models have cardinality ≤ ℵ₂. We now improve the work of [9] in two ways. Firstly, we prove that the consistency strength of the statement “CH and E F G ω ( , ) is determined for all models and of cardinality ℵ₂” is that of a weakly compact cardinal. On the other hand, we show that if 2 < 2 , T is a countable complete...

More reflections on compactness

Lúcia R. Junqueira, Franklin D. Tall (2003)

Fundamenta Mathematicae

We consider the question of when X M = X , where X M is the elementary submodel topology on X ∩ M, especially in the case when X M is compact.

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.

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