Propriétés de consistance et forcing
Propriétés de forcing et modèles génériques
Quantifier elimination for modules.
Quantifier elimination in quasianalytic structures via non-standard analysis
The paper is a continuation of an earlier one where we developed a theory of active and non-active infinitesimals and intended to establish quantifier elimination in quasianalytic structures. That article, however, did not attain full generality, which refers to one of its results, namely the theorem on an active infinitesimal, playing an essential role in our non-standard analysis. The general case was covered in our subsequent preprint, which constitutes a basis for the approach presented here....
Quantifier elimination, valuation property and preparation theorem in quasianalytic geometry via transformation to normal crossings
This paper investigates the geometry of the expansion of the real field ℝ by restricted quasianalytic functions. The main purpose is to establish quantifier elimination, description of definable functions by terms, the valuation property and preparation theorem (in the sense of Parusiński-Lion-Rolin). To this end, we study non-standard models of the universal diagram T of in the language ℒ augmented by the names of rational powers. Our approach makes no appeal to the Weierstrass preparation...
Quasi-axiomatic classes.
Quotients of Semi-Algebraic Spaces.
Ramified analysis and the minimal β-models of higher order arithmetics
Random orderings and unique ergodicity of automorphism groups
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner andWeiss’s example of the group of all permutations...
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.
ℳ-rank and meager types
Assume T is superstable and small. Using the multiplicity rank ℳ we find locally modular types in the same manner as U-rank considerations yield regular types. We define local versions of ℳ-rank, which also yield meager types.
Rational points on algebraic varieties over a generalized real closed field: a model theoretic approach.
Real classes in the ultrapower of hereditarily finite sets
Real closed exponential fields
Ressayre considered real closed exponential fields and “exponential” integer parts, i.e., integer parts that respect the exponential function. In 1993, he outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre’s construction and then analyze the complexity. Ressayre’s construction is canonical once we fix the real closed exponential field R, a residue field section k, and a well ordering ≺ on R. The...
Rectilinearization of functions definable by a Weierstrass system and its applications
This paper presents several theorems on the rectilinearization of functions definable by a convergent Weierstrass system, as well as their applications to decomposition into special cubes and quantifier elimination.
Recursive expansions
Let A be a recursive structure, and let ψ be a recursive infinitary sentence involving a new relation symbol. The main result of the paper gives syntactical conditions which are necessary and sufficient for every recursive copy of A to have a recursive expansion to a model of ψ, provided A satisfies certain decidability conditions. The decidability conditions involve a notion of rank. The main result is applied to prove some earlier results of Metakides-Nerode and Goncharov. In these applications,...
Recursive prime models for Boolean algebras
Reduced powers of -trees
Reduced products of infinite forcing systems.
Reduced Products Of Saturated Intuitionistic Theories