Lascar and Morley ranks differ in differentially closed fields
We note here, in answer to a question of Poizat, that the Morley and Lascar ranks need not coincide in differentially closed fields. We will approach this through the (perhaps) more fundamental issue of the variation of Morley rank in families. We will be interested here only in sets of finite Morl...
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| Format: | Journal article |
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Association for Symbolic Logic
1999
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| _version_ | 1797095021272367104 |
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| author | Hrushovski, E Scanlon, T |
| author_facet | Hrushovski, E Scanlon, T |
| author_sort | Hrushovski, E |
| collection | OXFORD |
| description | We note here, in answer to a question of Poizat, that the Morley and Lascar ranks need not coincide in differentially closed fields. We will approach this through the (perhaps) more fundamental issue of the variation of Morley rank in families. We will be interested here only in sets of finite Morley rank. Section 1 consists of some general lemmas relating the above issues. Section 2 points out a family of sets of finite Morley rank, whose Morley rank exhibits discontinuous upward jumps. To make the base of the family itself have finite Morley rank, we use a theorem of Buium. |
| first_indexed | 2024-03-07T04:22:04Z |
| format | Journal article |
| id | oxford-uuid:cb59719a-b2fb-437e-80a2-97fea0297001 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:22:04Z |
| publishDate | 1999 |
| publisher | Association for Symbolic Logic |
| record_format | dspace |
| spelling | oxford-uuid:cb59719a-b2fb-437e-80a2-97fea02970012022-03-27T07:14:11ZLascar and Morley ranks differ in differentially closed fieldsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cb59719a-b2fb-437e-80a2-97fea0297001Symplectic Elements at OxfordAssociation for Symbolic Logic1999Hrushovski, EScanlon, T We note here, in answer to a question of Poizat, that the Morley and Lascar ranks need not coincide in differentially closed fields. We will approach this through the (perhaps) more fundamental issue of the variation of Morley rank in families. We will be interested here only in sets of finite Morley rank. Section 1 consists of some general lemmas relating the above issues. Section 2 points out a family of sets of finite Morley rank, whose Morley rank exhibits discontinuous upward jumps. To make the base of the family itself have finite Morley rank, we use a theorem of Buium. |
| spellingShingle | Hrushovski, E Scanlon, T Lascar and Morley ranks differ in differentially closed fields |
| title | Lascar and Morley ranks differ in differentially closed fields |
| title_full | Lascar and Morley ranks differ in differentially closed fields |
| title_fullStr | Lascar and Morley ranks differ in differentially closed fields |
| title_full_unstemmed | Lascar and Morley ranks differ in differentially closed fields |
| title_short | Lascar and Morley ranks differ in differentially closed fields |
| title_sort | lascar and morley ranks differ in differentially closed fields |
| work_keys_str_mv | AT hrushovskie lascarandmorleyranksdifferindifferentiallyclosedfields AT scanlont lascarandmorleyranksdifferindifferentiallyclosedfields |