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(Almost strongly minimal) generalized n-gons are constructed for all n 3 for which the automorphism group acts transitively on the set of ordered ordinary (nj1)-gons contained in it, a new class of BN-pairs thus being obtained. Through the construction being modified slightly, 2 A ! many non-isomorphic almost strongly minimal generalized n-gons are obtained… (More)
We give a general criterion for the (bounded) simplicity of the automorphism groups of certain countable structures and apply it to show that the isometry group of the Urysohn space modulo the normal subgroup of bounded isometries is a simple group.
a r t i c l e i n f o a b s t r a c t Let M be a countably infinite first order relational structure which is homogeneous in the sense of Fraïssé. We show, under the assumption that the class of finite substructures of M has the free amalgamation property, along with the assumption that Aut(M) is transitive on M but not equal to Sym(M), that Aut(M) is a… (More)
We introduce a new notion of computable function on R N and prove some basic properties. We give two applications, first a short proof of Yoshinaga's theorem that periods are elementary (they are actually lower elementary). We also show that the lower elementary complex numbers form an algebraically closed field closed under exponentiation and some other… (More)
We show that any pseudofinite group with NIP theory and with a finite upper bound on the length of chains of centralisers is soluble-by-finite. In particular, any NIP rosy pseudofinite group is soluble-by-finite. This generalises, and shortens the proof of, an earlier result for stable pseudofinite groups. An example is given of an NIP pseudofinite group… (More)
We give a description of infinite families of finite primitive permutation groups for which there is a uniform finite upper bound on the diameter of all orbital graphs. This is equivalent to describing families of finite permutation groups such that every ultraproduct of the family is primitive. A key result is that, in the almost simple case with socle of… (More)