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A unified approach to the theory of normed structures - Part I: The single-sorted case

Abstract

We introduce the concept of a prenormed model of a particular kind of single-sorted finitary first-order theories, that we refer to as prealgebraic theories. These are characterized by a signature comprising, together with arbitrary function symbols, only relation symbols whose interpretation, in any possible model, is a preorder. The result is an abstract approach to the notion of norm and, consequently, to the theory of normed structures.
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Dates and versions

hal-00696491 , version 1 (11-05-2012)
hal-00696491 , version 2 (14-05-2012)
hal-00696491 , version 3 (22-05-2012)

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Salvatore Tringali. A unified approach to the theory of normed structures - Part I: The single-sorted case. 2012. ⟨hal-00696491v2⟩
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