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Preprint Number 247
247. Cédric Milliet
Infinitely Definable Algebraic Structures in Small Theories
Submission date: 8 May 2010.
We observe simple links between preorders,
semi-groups, 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 n-types for each integer n. A category defined by a pure n-type
in a small structure is the conjunction of definable categories. For a
group G_A defined by an n-type 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, semi-groups, rings and categories, field, ring, preodred, equivalence relation, category groupoid.
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