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Groupoids, imaginaries and internal covers

Ehud Hrushovski
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Abstract

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.

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Ehud Hrushovski. 2006-03-16. Groupoids, imaginaries and internal covers. https://arxiv.org/abs/math/0603413

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