Decompositions of saturated models of stable theories
We characterize the stable theories T for which the saturated models of T admit decompositions. In particular, we show that countable, shallow, stable theories with NDOP have this property.
Dense pairs of o-minimal structures
The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of "small definable set" plays a special role in this description.
Elementary submodels of parametrizable models.
Exercices sur la stabilité
Existentially closed II₁ factors
We examine the properties of existentially closed (-embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed (-embeddable) II₁ factor is approximately inner to prove that Th() is not model-complete. We also show that Th() is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th().
Fiberwise properties of definable sets and functions in o-minimal structures.
Graphs and models with finite chains.
Homogeneous limit reduced powers.
Homogeneous models and generic extensions.
Homogeneous models and stable diagrams.
Homogeneous-Universal Models of Theories Which Have Model Completions
Locally finite theories with model companion
Si dà, mediante condizioni per l'amalgamabilità di tre modelli, una caratterizzazione completa delle teorie localmente finite con model-compagno. Si introduce inoltre un concetto intermedio tra quelli di model-compagno e model-completamento.
Model-theoretical constructions in AST. I.
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.