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-amalg...
| Hlavní autor: | |
|---|---|
| Médium: | Journal article |
| Vydáno: |
2011
|
| _version_ | 1826298720319176704 |
|---|---|
| author | Hrushovski, E |
| author_facet | Hrushovski, E |
| author_sort | Hrushovski, E |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T04:51:07Z |
| format | Journal article |
| id | oxford-uuid:d4fde2c9-1c13-457d-9e41-b1a00fc5ce63 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:51:07Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:d4fde2c9-1c13-457d-9e41-b1a00fc5ce632022-03-27T08:22:48ZGroupoids, imaginaries and internal coversJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d4fde2c9-1c13-457d-9e41-b1a00fc5ce63Symplectic Elements at Oxford2011Hrushovski, ELet $T$ 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. |
| spellingShingle | Hrushovski, E Groupoids, imaginaries and internal covers |
| title | Groupoids, imaginaries and internal covers |
| title_full | Groupoids, imaginaries and internal covers |
| title_fullStr | Groupoids, imaginaries and internal covers |
| title_full_unstemmed | Groupoids, imaginaries and internal covers |
| title_short | Groupoids, imaginaries and internal covers |
| title_sort | groupoids imaginaries and internal covers |
| work_keys_str_mv | AT hrushovskie groupoidsimaginariesandinternalcovers |