We introduce the notion of a lovely pair of models of a simple theory T , generalizing Poizat’s “belles paires” of models of a stable theory and the third author’s “generic pairs” of models of an SU -rank 1 theory. We characterise when a saturated model of the theory TP of lovely pairs is a lovely pair (that is when the notion of a lovely pair is “axiomatizable”), finding an analogue of the non...

We prove that a non-abelian superstable CSA-group has an infinite definable simple subgroup all of whose proper definable subgroups are abelian. This imply in particular that the existence of non-abelian CSAgroup of finite Morley rank is equivalent to the existence of a simple bad group all whose definable proper subgroups are abelian. We give a new proof of a result of E. Mustafin and B. Poiza...

The (countable) perturbed existentially closed graph S (Gordinowicz, 2010 [5]) was introduced by the second author as a solution to a problem stated by Bonato (Problem 20 in Cameron (2003) [3]). The graph S is not isomorphic to the Rado graph, nevertheless it has theNNc property in the sense that subgraphs induced by the neighbourhood and by the non-neighbourhood of each vertex ofS are isomorph...

Themonotone constraint satisfaction problem (MCSP) is the problem of, given an existentially quantified positive formula, decide whether this formula has a model. This problem is a natural generalization of the constraint satisfaction problem, which can be seen as the problem of determining whether a conjunctive formula has a model. In this paper we study the worst-case time complexity, measure...