Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1001-91
Keywords
Internal cover, groupoid, higher amalgamation, elimination of imaginaries, pseudo-finite fields
First Page
173
Last Page
198
Recommended Citation
HRUSHOVSKI, E (2012). Groupoids, imaginaries and internal covers. Turkish Journal of Mathematics 36 (2): 173-198. https://doi.org/10.3906/mat-1001-91