On the number of generic models
On the problem of axiomatization of tame representation type
Associative algebras of fixed dimension over algebraically closed fields of fixed characteristic are considered. It is proved that the class of algebras of tame representation type is axiomatizable. Moreover, finite axiomatizability of this class is equivalent to the conjecture that the algebras of tame representation type form a Zariski-open subset in the variety of algebras.
On the problem of finite signature.
On the Quantifier of Limiting Realizability
On the relation of -reducibility between admissible sets.
On the relationship between weak compactness in L... and restricted second-order languages.
On the simplicity and subdirect irreducibility of Boolean ultrapowers
On two complete sets in the analytical and the arithmetical hierarchies.
On two tame algebras with super-decomposable pure-injective modules
Let k be a field of characteristic different from 2. We consider two important tame non-polynomial growth algebras: the incidence k-algebra of the garland 𝒢₃ of length 3 and the incidence k-algebra of the enlargement of the Nazarova-Zavadskij poset 𝒩 𝓩 by a greatest element. We show that if Λ is one of these algebras, then there exists a special family of pointed Λ-modules, called an independent pair of dense chains of pointed modules. Hence, by a result of Ziegler, Λ admits a super-decomposable...
On variants of CM-triviality
We introduce a generalisation of CM-triviality relative to a fixed invariant collection of partial types, in analogy to the Canonical Base Property defined by Pillay, Ziegler and Chatzidakis which generalises one-basedness. We show that, under this condition, a stable field is internal to the family, and a group of finite Lascar rank has a normal nilpotent subgroup such that the quotient is almost internal to the family.
On -subsets of naturals over abelian groups.
On -categorical theories of abelian groups
On -categorical theories of fields
Orbits of denumerable models of complete theories
Order-types of models of arithmetic and a connection with arithmetic saturation.