8,809 research outputs found

    A presentation theorem for continuous logic and Metric Abstract Elementary Classes

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    We give a presentation theorem for continuous first-order logic and Metric Abstract Elementary classes in terms of Lω1,ωL_{\omega_1, \omega} and Abstract Elementary Classes, respectively. This presentation is accomplished by analyzing dense subsets that are closed under functions. We extend this correspondence to types and saturation

    Modular functionals and perturbations of Nakano spaces

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    We settle several questions regarding the model theory of Nakano spaces left open by the PhD thesis of Pedro Poitevin \cite{Poitevin:PhD}. We start by studying isometric Banach lattice embeddings of Nakano spaces, showing that in dimension two and above such embeddings have a particularly simple and rigid form. We use this to show show that in the Banach lattice language the modular functional is definable and that complete theories of atomless Nakano spaces are model complete. We also show that up to arbitrarily small perturbations of the exponent Nakano spaces are ℵ0\aleph_0-categorical and ℵ0\aleph_0-stable. In particular they are stable
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