A singular hyperbolic set is a partially hyperbolic set with singularities (all hyper-bolic) and volume expanding central direction [MPP1]. We study connected, singular-hyperbolic, attracting sets with dense closed orbits and only one singularity. These sets are shown to be transitive for most C r flows in the Baire's second category sence. In general these sets are shown to be either transitiv...

Moufang sets are split doubly transitive permutation groups, or equivalently, groups with a split BN-pair of rank one. In this paper, we study so-called special Moufang sets with abelian root groups, under the model-theoretic restriction that the groups have finite Morley rank. These groups have a natural base field, and we classify them under the additional assumption that the base field is in...

In Zermelo-Fraenkel set theory with the axiom of choice every set has the same cardinal number as some ordinal. Von Rimscha has weakened this condition to “Every set has the same cardinal number as some transitive set.” In set theory without the axiom of choice, we study the deductive strength of this and similar statements introduced by von Rimscha. We shall use the standard notation and termi...

In this paper we construct transitive t-designs from the linear groups L(2, q), q ≤ 23. Thereby we classify t-designs, t ≥ 2, admitting a transitive action of the linear groups L(2, q), q ≤ 23, up to 35 points and obtained numerous transitive designs, for 36 ≤ v ≤ 55. In many cases we proved the existence of t-designs with certain parameter sets. Among others we constructed t-designs with param...