Generalizing and unifying the known theorems for difference and differential fields, it is shown that for every finite free algebra scheme.

In this paper, it is shown that if [Formula: see text] is a complete type of Lascar rank at least 2, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations [Formula: see text], [Formula: see text] such that p has a nonalgebraic forking extension over [Formula: see text]. Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over [Formula: see text]. The results are (...) also formulated in a more general setting. (shrink)

Zoé Chatzidakis , David Marker , Amador Martin-Pizarro , Rahim Moosa , Sergei Starchenko Source: Notre Dame J. Formal Logic, Volume 54, Number 3-4, 277--277.

An amalgamation base p in a simple theory is stably definable if its canonical base is interdefinable with the set of canonical parameters for the ϕ-definitions of p as ϕ ranges through all stable formulae. A necessary condition for stably definability is given and used to produce an example of a supersimple theory with stable forking having types that are not stably definable. This answers negatively a question posed in [8]. A criterion for and example of a stably definable amalgamation (...) base whose restriction to the canonical base is not axiomatised by stable formulae are also given. The examples involve generic relations over non CM-trivial stable theories. (shrink)

We characterise strongly minimal groups interpretable in elementary extensions of compact complex analytic spaces.