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| Format: | Preprint |
| Published: |
2006
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0603413 |
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| _version_ | 1866910545741873152 |
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| author | Hrushovski, Ehud |
| author_facet | Hrushovski, Ehud |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0603413 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | Groupoids, imaginaries and internal covers Hrushovski, Ehud Logic Category Theory 03C07 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. |
| title | Groupoids, imaginaries and internal covers |
| topic | Logic Category Theory 03C07 |
| url | https://arxiv.org/abs/math/0603413 |