Interpreting groups and fields in some nonelementary classes
| dc.creator | Hyttinen, Tapani | |
| dc.creator | Lessmann, Olivier | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2004-06-23 | |
| dc.date.accessioned | 2026-07-07T05:09:31Z | |
| dc.date.available | 2026-07-07T05:09:31Z | |
| dc.description | This paper is concerned with extensions of geometric stability theory to some nonelementary classes. We prove the following theorem: Theorem: Let C be a large homogeneous model of a stable diagram D. Let p, q in S_D(A), where p is quasiminimal and q unbounded. Let P=p(C) and Q=q(C). Suppose that there exists an integer n<omega such that dim(a_1...a_n/A cup C)=n, for any independent a_1,..., a_n in P and finite subset C subseteq Q, but dim(a_1...a_n a_{n+1}/A cup C) <= n, for some independent a_1,...,a_n,a_{n+1} in P and some finite subset C subseteq Q. Then C interprets a group G which acts on the geometry P' obtained from P. Furthermore, either C interprets a non-classical group, or n=1,2,3 and * If n=1 then G is abelian and acts regularly on P'. * If n=2 the action of G on P' is isomorphic to the affine action of K times K^* on the algebraically closed field K. * If n = 3 the action of G on P' is isomorphic to the action of PGL_2(K) on the projective line {P}^1(K) of the algebraically closed field K . | |
| dc.identifier | https://arxiv.org/abs/math/0406481 | |
| dc.identifier | http://arxiv.org/abs/math/0406481 | |
| dc.identifier | J. Math. Log. 5 No. 1 (2005) 1--47 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71653 | |
| dc.subject | Logic | |
| dc.title | Interpreting groups and fields in some nonelementary classes | |
| dc.type | text |