Name
Abstract | ||
|---|---|---|
Given any field K, there is a function field F/K in one variable containing definable transcendentals over K, i.e.. elements in F \ K first-order definable in the language of fields with parameters from K, Hence, the model-theorctic and the field-theoretic relative algebraic closure of K in F do not coincide. E.g., if K is finite, the model-theoretic algebraic closure of K in the rational function field K(t) s K(t). For the proof, diophantine phi-definability of K in F is established for any function field F/K in one variable, provided K is large, or K (x) /(K-x) is finite for some integer n > 1 coprime to char K. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.2178/jsl/1190150142 | JOURNAL OF SYMBOLIC LOGIC |
DocType | Volume | Issue |
Journal | 67 | 3 |
ISSN | Citations | PageRank |
0022-4812 | 2 | 0.45 |
References | Authors | |
0 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jochen Koenigsmann | 1 | 10 | 2.31 |