An alternative proof of the ultralimits theorem.
An analysis of Karp’s interpolation theorem and the notion of -consistency property
An application of a reflection principle
We define a recursive theory which axiomatizes a class of models of IΔ₀ + Ω ₃ + ¬ exp all of which share two features: firstly, the set of Δ₀ definable elements of the model is majorized by the set of elements definable by Δ₀ formulae of fixed complexity; secondly, Σ₁ truth about the model is recursively reducible to the set of true Σ₁ formulae of fixed complexity.
An application of higher order fixed points of normal functions.
An application of the Ehrenfeucht-Fraisse game in formal language theory
An autostable 2 nilpotent group with no Scott family of finitary formulas.
An elementary class extending abelian-by- groups, for infinite
We show that for no infinite group the class of abelian-by- groups is elementary, but, at least when is an infinite elementary abelian -group (with prime), the class of groups admitting a normal abelian subgroup whose quotient group is elementarily equivalent to is elementary.
An essay on model theory
Some basic ideas of model theory are presented and a personal outlook on its perspectives is given.
An expansion of an -categorical model
An intensional approach to questions
An intuitionistic logic with probablistic operators.
An intuitionistic omitting types theorem.
An Intuitionistic Ommiting Types Theorem
An invariant for difference field extensions
In this paper we introduce a new invariant for extensions of difference fields, the distant degree, and discuss its properties.
An irrational problem
Given a topological space ⟨X,⟩ ∈ M, an elementary submodel of set theory, we define to be X ∩ M with topology generated by . Suppose is homeomorphic to the irrationals; must ? We have partial results. We also answer a question of Gruenhage by showing that if is homeomorphic to the “Long Cantor Set”, then .
An o-minimal structure which does not admit cellular decomposition
We present an example of an o-minimal structure which does not admit cellular decomposition. To this end, we construct a function whose germ at the origin admits a representative for each integer , but no representative. A number theoretic condition on the coefficients of the Taylor series of then insures the quasianalyticity of some differential algebras induced by . The o-minimality of the structure generated by is deduced from this quasianalyticity property.
An Omitting Types Theorem with an Application to the Construction of Generic Structures.
An ordered structure of rank two related to Dulac's Problem
For a vector field ξ on ℝ² we construct, under certain assumptions on ξ, an ordered model-theoretic structure associated to the flow of ξ. We do this in such a way that the set of all limit cycles of ξ is represented by a definable set. This allows us to give two restatements of Dulac’s Problem for ξ - that is, the question whether ξ has finitely many limit cycles-in model-theoretic terms, one involving the recently developed notion of -rank and the other involving the notion of o-minimality.
An ordering of normal ultrafiltres
An Ordering of the set of Sentences of Peano Arithmetic