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Preprint Number 247
247. Cédric Milliet Infinitely Definable Algebraic Structures in Small Theories Email: Submission date: 8 May 2010. Abstract: We observe simple links between preorders,
semigroups, rings and categories (and between equivalence relations,
groups, fields and groupoids), which are infinitely definable in an
arbitrary structure, and apply these observations to small
structures. Recall that a structure is small if it has countably many
pure ntypes for each integer n. A category defined by a pure ntype
in a small structure is the conjunction of definable categories. For a
group G_A defined by an ntype over some arbitrary set A in a small
and simple structure, we deduce that Mathematics Subject Classification: 03C45, 03C60, 20L05, 20M99. Keywords and phrases: Small theory, simple theory, infinitely definable, semigroups, rings and categories, field, ring, preodred, equivalence relation, category groupoid. Full text: pdf.

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