o-minimality.
On a proof of the Erdős-Monk theorem.
On acyclic hypergraphs of minimal prime models.
On elementary cuts in recursively saturated models of Peano Arithmetic
On embedding models of arithmetic of cardinality ℵ₁ into reduced powers
In the early 1970’s S. Tennenbaum proved that all countable models of PA₁¯ + ∀₁ -Th(ℕ) are embeddable into the reduced product , where ℱ is the cofinite filter. In this paper we show that if M is a model of PA¯ + ∀₁ - Th(ℕ), and |M| = ℵ₁, then M is embeddable into , where D is any regular filter on ω.
On extending automorphisms of models of Peano Arithmetic
Continuing the earlier research in [10] we give some information on extending automorphisms of models of PA to end extensions and cofinal extensions.
On Minimal Ordered Structures
On nonstructure of elementary submodels of a stable homogeneous structure
We assume that M is a stable homogeneous model of large cardinality. We prove a nonstructure theorem for (slightly saturated) elementary submodels of M, assuming M has dop. We do not assume that th(M) is stable.
On probability of first order formulas in a given model
On semialgebraic points of definable sets
We prove that the semialgebraic, algebraic, and algebraic nonsingular points of a definable set in o-minimal structure with analytic cell decomposition are definable. Moreover, the operation of taking semialgebraic points is idempotent and the degree of complexity of semialgebraic points is bounded.
On sets with rank one in simple homogeneous structures
We study definable sets D of SU-rank 1 in , where ℳ is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a ’canonically embedded structure’, which inherits all relations on D which are definable in , and has no other definable relations. Our results imply that if no relation symbol of the language of ℳ has arity higher than 2, then there is a close relationship between triviality of dependence and being a reduct of a binary...