Seminários de Lógica Matemática

26 de Março 2009, 18h00

Geometric structures and weak local modularity. (Joint work with Evgueni Vassiliev)
Complexo Interdisciplinar, Sala B3-01

ALEXANDER BERENSTEIN Universidad de Los Andes, Bogota and Université Claude Bernard Lyon I)

Abstract:

A theory T is called geometric if for all models of T, the algebraic closure satisfies the exchange property and if it eliminates the quantifier $\exists^\infty$. Examples include strongly minimal theories and o-minimal theories extending DLO. In this theories there is a natural notion of dimension of a set. It is well know that linear strongly minimal theories are locally modular (admit a group-like pre-geometry), but that o-minimal linear theories need not be locally modular. We define a notion of weak local modularity that agrees with local modularity in strongly minimal theories and linearity in o-minimal theories.

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