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...
P-NDOP and P-decompositions of -saturated models of superstable theories
Given a complete, superstable theory, we distinguish a class P of regular types, typically closed under automorphisms of ℭ and non-orthogonality. We define the notion of P-NDOP, which is a weakening of NDOP. For superstable theories with P-NDOP, we prove the existence of P-decompositions and derive an analog of the first author's result in Israel J. Math. 140 (2004). In this context, we also find a sufficient condition on P-decompositions that implies non-isomorphic models. For this, we investigate...
ℳ-rank and meager groups
Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.
Relations between Shy Sets and Sets of -Measure Zero in Solovay’s Model
An example of a non-zero non-atomic translation-invariant Borel measure on the Banach space is constructed in Solovay’s model. It is established that, for 1 ≤ p < ∞, the condition "-almost every element of has a property P" implies that “almost every” element of (in the sense of [4]) has the property P. It is also shown that the converse is not valid.
Rigid -saturated models of superstable theories
In a countable superstable NDOP theory, the existence of a rigid -saturated model implies the existence of rigid -saturated models of power λ for every .
Saturated Boolean Algebras With Ultrafilters
Saturated Boolean algebras with ultrafilters.
Some automorphisms of natural numbers in the alternative set theory
Some model theory of simple algebraic groups over algebraically closed fields
Some Questions Concerning Minimal Structures
Some remarks on well-ordered models
Structure of algebraic systems with a complete theory of infinite subsystems.
Suites d'indicernables dans les théories stables
The theorems of Beth and Craig in abstract model theory. II. Compact logics.
Type d'ordre des ordinaux de modèles non dénombrables de la théorie des ensembles
Une théorie finiement axiomatisable et superstable