More on locally atomic models
By results of [9] there are models and for which the Ehrenfeucht-Fraïssé game of length ω₁, , 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 is determined for all models and of cardinality ℵ₂” is that of a weakly compact cardinal. On the other hand, we show that if , T is a countable complete...
We consider the question of when , where is the elementary submodel topology on X ∩ M, especially in the case when is compact.
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 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.