Ni konstruas nun malbonajn korpojn, kun malfinita Morleya ranko, kiuj estas ricevitaj per memsuficanta amalgameco de korpoj kun unara predikato nomanta sumigan au obligan subgrupon, ciam lau la Hrushovskija maniero. Al uzado de ciuj kiuj la anglujon malkonprenas, tiel tradukigas la supera citajo : "Estas prava ke tiu ci kiu kun la sago interrilatigas, la sagecon rikoltas". Gustatempe, la autoro varmege dankas ciujn kiuj la korektan citajon sendis al li, speciale la unuan respondinton : David KUEKER.

AssumeGis a group definable in a modelMof a stable theoryT. We prove that the semigroupSG(M) of completeG-types overMis an inverse limit of some semigroups type-definable inMeq. We prove that the maximal subgroups ofSG(M) are inverse limits of some definable quotients of subgroups ofG. We consider the powers of types in the semigroupSG(M) and prove that in a way every type inSG(M) is profinitely many steps away from a type in a subgroup ofSG(M).

We interpret the basic notions of topological dynamics in the model-theoretic setting, relating them to generic types of definable group actions and their generalizations.

T is stable. We define the notion of meager regular type and prove that a meager regular type is locally modular. Assuming I < 2o and G is a definable abelian group with locally modular regular generics, we prove a counterpart of Saffe's conjecture. Using these results, for superstable T we prove the conjecture of vanishing multiplicities. Also, as a further application, in some additional cases we prove a conjecture regarding topological stability of pseudo-types over Q.

Assume T is a superstable theory with $ countable models. We prove that any *-algebraic type of M-rank > 0 is m-nonorthogonal to a *-algebraic type of M-rank 1. We study the geometry induced by m-dependence on a *-algebraic type p* of M-rank 1. We prove that after some localization this geometry becomes projective over a division ring F. Associated with p* is a meager type p. We prove that p is determined by p* up to nonorthogonality and that F (...) underlies also the geometry induced by forking dependence on any stationarization of p. Also we study some *-algebraic *-groups of M-rank 1 and prove that any *-algebraic *-group of M-rank 1 is abelian-by-finite. (shrink)

AssumeTis a superstable theory with 0 is m-nonorthogonal to a *-algebraic type of-rank 1. We study the geometry induced by m-dependence on a *-algebraic typep*of-rank 1. We prove that after some localization this geometry becomes projective over a division ring. Associated withp*is a meager typep. We prove thatpis determined byp*up to nonorthogonality and thatunderlies also the geometry induced by forking dependence on any stationarization ofp. Also we study some *-algebraic *-groups of-rank 1 and prove that any *-algebraic *-group of-rank 1 (...) is abelian-by-finite. (shrink)

Assume G is a superstable locally modular group. We describe for any countable model M of Th(G) the quotient group G(M) / Gm(M). Here Gm is the modular part of G. Also, under some additional assumptions we describe G(M) / Gm(M) relative to G⁻(M). We prove Vaught's Conjecture for Th(G) relative to Gm and a finite set provided that ℳ(G) = 1 and the ring of pseudoendomorphisms of G is finite.