Groupoids, imaginaries and internal covers

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.

Anahtar Kelimeler:

Internal cover, groupoid, higher amalgamation, elimination of imaginaries, pseudo-finite fields

Groupoids, imaginaries and internal covers

Keywords:

Internal cover, groupoid, higher amalgamation, elimination of imaginaries, pseudo-finite fields,

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