Name
Abstract | ||
|---|---|---|
We discuss the connection between decidability of a theory of a large algebraic extensions of Q and the recursiveness of the field as a subset of a fixed algebraic closure. In particular, we prove that if an algebraic extension K of Q has a decidable existential theory, then within any fixed algebraic closure (Q) over tilde of Q, the field K must be conjugate over Q to a field which is recursive as a subset of the algebraic closure. We also show that for each positive integer e there are infinitely many e-tuples sigma is an element of Gal(Q)(e) such that the field (Q) over tilde(sigma) is primitive recursive in (Q) over tilde and its elementary theory is primitive recursively decidable. Moreover, (Q) over tilde(sigma) is PAC and Gal((Q) over tilde(sigma)) is isomorphic to the free profinite group on e generators. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1017/jsl.2017.10 | JOURNAL OF SYMBOLIC LOGIC |
Keywords | DocType | Volume |
decidable theory,recursive subsets | Journal | 82 |
Issue | ISSN | Citations |
2 | 0022-4812 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Moshe Jarden | 1 | 1 | 1.73 |
| Alexandra Shlapentokh | 2 | 12 | 8.14 |