We give a complete description of minimal groups infinitely definable in separably closed fields of finite degree of imperfection. In particular we answer positively the question of the existence of such a group with infinite transcendence degree (i.e., a minimal group with non thin generic).

We give a reduction of the function field Mordell–Lang conjecture to the function field Manin–Mumford conjecture, for abelian varieties, in all characteristics, via model theory, but avoiding recourse to the dichotomy theorems for Zariski geometries. Additional ingredients include the “Theorem of the Kernel”, and a result of Wagner on commutative groups of finite Morley rank without proper infinite definable subgroups. In positive characteristic, where the main interest lies, there is one more crucial ingredient: “quantifier-elimination” for the corresponding [Formula: see text] (...) where [Formula: see text] is a saturated separably closed field. (shrink)

We show that if G is a strongly minimal finitely axiomatizable group, the division ring of quasi-endomorphisms of G must be an infinite finitely presented ring.

Father Bouscaren, professor of Logic and Ontology in the St. Louis Unversity School of Philosophy, has made a penetrating study of the knotty problem of the veracity of the senses. This is the first article in an important series. The Editor.

We consider the question of when, given a subset A of M, the setwise stabilizer of the group of automorphisms induces a closed subgroup on Sym(A). We define s-homogeneity to be the analogue of homogeneity relative to strong embeddings and show that any subset of a countable, s-homogeneous, ω-stable structure induces a closed subgroup and contrast this with a number of negative results. We also show that for ω-stable structures s-homogeneity is preserved under naming countably many constants, but under slightly (...) weaker conditions it can be lost by naming a single point. (shrink)

Father Bouscaren, professor of Logic and Ontology in the St. Louis Unversity School of Philosophy, has made a penetrating study of the knotty problem of the veracity of the senses. This is the first article in an important series. The Editor.

THIS is the second article in an important series which has been attracting considerable attention. Its topic is a problem grey with centuries. The Editor.