Portal de Periódicos da CAPES

Groupoids, imaginaries and internal covers

2012; Scientific and Technological Research Council of Turkey (TUBITAK); Volume: 36; Issue: 2 Linguagem: Inglês

1303-6149

Ehud Hrushovski,

Geometric and Algebraic Topology

Let T be a first-order theory. A correspondence is established between internal covers of models of T and definable groupoids within T. We also consider amalgamations of independent diagrams of algebraically closed substructures, and find strong relation between covers, uniqueness for 3-amalgamation, existence of 4-amalgamation, imaginaries of T\si, and definable groupoids. As a corollary, we describe the imaginary elements of families of finite-dimensional vector spaces over pseudo-finite fields.