# Modular functionals and perturbations of Nakano spaces - Mathematics > Logic

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Abstract: We settle several questions regarding the model theory of Nakano spaces leftopen by the PhD thesis of Pedro Poitevin \cite{Poitevin:PhD}. We start bystudying isometric Banach lattice embeddings of Nakano spaces, showing that indimension two and above such embeddings have a particularly simple and rigidform. We use this to show show that in the Banach lattice language the modularfunctional is definable and that complete theories of atomless Nakano spacesare model complete. We also show that up to arbitrarily small perturbations ofthe exponent Nakano spaces are \$\aleph 0\$-categorical and \$\aleph 0\$-stable. Inparticular they are stable.

Autor: Itaï Ben Yaacov ICJ

Fuente: https://arxiv.org/