On -categoricity and the theory of trees
On a universal axiomatization of the real closed fields
This paper presents a natural axiomatization of the real closed fields. It is universal and admits quantifier elimination.
On acyclic hypergraphs of minimal prime models.
On clones determined by their initial segments
On elementary equivalence of abelian groups
On expansions of β-models
On models of arithmetic having non-modular substructure lattices
On Ø-definable elements in a field
We develop an arithmetic characterization of elements in a field which are first-order definable by a parameter-free existential formula in the language of rings. As applications we show that in fields containing any algebraically closed field only the elements of the prime field are existentially ∅-definable. On the other hand, many finitely generated extensins of Q contain existentially ∅-definable elements which are transcendental over Q. Finally, we show that all transcendental elements in...
On places of algebraic function fields.
On relational selections for complete theories.
On some conjectures connected with complete sentences
On some elementary properties of soluble groups of derived length 2.
On some model theoretic problems concerning certain extensions of abelian groups by groups of finite exponent
On the Axiomatizability of Certain Classes of Modules.
On the congruence lattice of stable algebras with definability of compact congruences
On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth
Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.
On The Greatest Congruence Of Relations
On the greatest congruence of relations.
On the model companion for e-fold p-adically valued fields.
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.