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Article Dans Une Revue Journal of Logic and Analysis Année : 2009

Modular functionals and perturbations of Nakano spaces

Résumé

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 $\aleph_0$-categorical and $\aleph_0$-stable. In particular they are stable.
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Dates et versions

hal-00259298 , version 1 (27-02-2008)
hal-00259298 , version 2 (26-01-2009)
hal-00259298 , version 3 (23-02-2009)

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Citer

Itaï Ben Yaacov. Modular functionals and perturbations of Nakano spaces. Journal of Logic and Analysis, 2009, 1 (1), pp.1-42. ⟨10.4115/jla.2009.1.1⟩. ⟨hal-00259298v3⟩
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