The paper introduces an analogue of the Reid class for Banach spaces over valued fields, verifies a classification theorem for its structural hierarchy, and applies it to distinguish specific C_p-spaces and limit their expressibility via direct sums and products.
Non-Archimedean Analogue of Chase's Lemma
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abstract
We formulate and verify a non-Archimedean analogue of Chase's lemma. Following the framework by K.\ Eda removing restriction of cardinality from analogy on direct product between countability and non-$\omega_1$-measurability, we extend the non-Archimedean analogue of Chase's lemma to a non-Archimedean counterpart of the extension by K.\ Eda of the extension by M.\ Dugas and B.\ Zimmermann-Huisgen of Chase's lemma.
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math.LO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Structural Hierarchy of Reid Class of non-Archimedean Banach Spaces
The paper introduces an analogue of the Reid class for Banach spaces over valued fields, verifies a classification theorem for its structural hierarchy, and applies it to distinguish specific C_p-spaces and limit their expressibility via direct sums and products.