Groupoids, imaginaries and internal covers

Details Groupoids, imaginaries and internal covers Groupoids, imaginaries and internal covers

2006-03-16

arxiv.org/abs/math/0603413v3

Mathematics

Logic

Local improvements; thanks to referee of Turkish Mathematical Journal. First appeared in the proceedings of the Paris VII semi

Scientific paper

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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