1,382 research outputs found
Fields and Fusions: Hrushovski constructions and their definable groups
An overview is given of the various expansions of fields and fusions of
strongly minimal sets obtained by means of Hrushovski's amalgamation method, as
well as a characterization of the groups definable in these structures
Dimensional groups and fields
We shall define a general notion of dimension, and study groups and rings
whose interpretable sets carry such a dimensio. In particular, we deduce chain
conditions for groups, definability results for fields and domains, and show
that pseudofinite groups contain big finite-by-abelian subgroups, and
pseudofinite groups of dimension 2 contain big soluble subgroups
The right angle to look at orthogonal sets
If X and Y are orthogonal hyperdefinable sets such that X is simple, then any
group G interpretable in (X,Y) has a normal hyperdefinable X-internal subgroup
N such that G/N is Y-internal; N is unique up to commensurability. In order to
make sense of this statement, local simplicity theory for hyperdefinable sets
is developped. Moreover, a version of Schlichting's Theorem for hyperdefinable
families of commensurable subgroups is shown
Quelques réflexions inévitables (Some inevitable considerations)
International audienceWe generalize Frécon's construction of the inevitable radical to groups in stable and even simple theories
Plus ultra
International audienceWe define a reasonably well-behaved class of ultraimaginaries, i.e.\ classes modulo invariant equivalence relations, called {\em tame}, and establish some basic simplicity-theoretic facts. We also show feeble elimination of supersimple ultraimaginaries: If is an ultraimaginary definable over a tuple with , then is eliminable up to rank . Finally, we prove some uniform versions of the weak canonical base property
- …