On a question of Abraham Robinson
In this note we give a negative answer to Abraham Robinson’s question of whether a finitely generated extension of an undecidable field is always undecidable. We construct ‘natural’ undecidable fields of transcendence degree 1 over Q all of whose proper finite extensions are decidable. We also const...
| Autor principal: | |
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| Formato: | Journal article |
| Publicado em: |
Hebrew University Magnes Press
2016
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| _version_ | 1826297146224148480 |
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| author | Koenigsmann, J |
| author_facet | Koenigsmann, J |
| author_sort | Koenigsmann, J |
| collection | OXFORD |
| description | In this note we give a negative answer to Abraham Robinson’s question of whether a finitely generated extension of an undecidable field is always undecidable. We construct ‘natural’ undecidable fields of transcendence degree 1 over Q all of whose proper finite extensions are decidable. We also construct undecidable algebraic extensions of Q that allow decidable finite extensions. |
| first_indexed | 2024-03-07T04:27:07Z |
| format | Journal article |
| id | oxford-uuid:cd085f2a-30c2-41a5-9d56-106d218b8279 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:27:07Z |
| publishDate | 2016 |
| publisher | Hebrew University Magnes Press |
| record_format | dspace |
| spelling | oxford-uuid:cd085f2a-30c2-41a5-9d56-106d218b82792022-03-27T07:25:57ZOn a question of Abraham RobinsonJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cd085f2a-30c2-41a5-9d56-106d218b8279Symplectic Elements at OxfordHebrew University Magnes Press2016Koenigsmann, JIn this note we give a negative answer to Abraham Robinson’s question of whether a finitely generated extension of an undecidable field is always undecidable. We construct ‘natural’ undecidable fields of transcendence degree 1 over Q all of whose proper finite extensions are decidable. We also construct undecidable algebraic extensions of Q that allow decidable finite extensions. |
| spellingShingle | Koenigsmann, J On a question of Abraham Robinson |
| title | On a question of Abraham Robinson |
| title_full | On a question of Abraham Robinson |
| title_fullStr | On a question of Abraham Robinson |
| title_full_unstemmed | On a question of Abraham Robinson |
| title_short | On a question of Abraham Robinson |
| title_sort | on a question of abraham robinson |
| work_keys_str_mv | AT koenigsmannj onaquestionofabrahamrobinson |