Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander
Restrictions on the degree spectra of algebraic structures.
Results on automorphisms of recursively saturated models of PA
Rich families and elementary submodels
We compare two methods of proving separable reduction theorems in functional analysis - the method of rich families and the method of elementary submodels. We show that any result proved using rich families holds also when formulated with elementary submodels and the converse is true in spaces with fundamental minimal system and in spaces of density ℵ1. We do not know whether the converse is true in general. We apply our results to show that a projectional skeleton may be without loss of generality...
Rigid subanalytic sets
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 .
Rigidity, internality and analysability
We prove a version of Hrushovski's Socle Lemma for rigid groups in an arbitrary simple theory.
Robust neural network control of robotic manipulators via switching strategy
In this paper, a robust neural network control scheme for the switching dynamical model of the robotic manipulators has been addressed. Radial basis function (RBF) neural networks are employed to approximate unknown functions of robotic manipulators and a compensation controller is designed to enhance system robustness. The weight update law of the robotic manipulator is based on switched multiple Lyapunov function method and the periodically switching law which is suitable for practical implementation...
Rosenthal compacta and NIP formulas
We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about ϕ-types for ϕ NIP. In particular, we show that if M is a countable model, then an M-invariant ϕ-type is Borel-definable. Also, the space of M-invariant ϕ-types is a Rosenthal compactum, which implies a number of topological tameness properties.
-Rings and -Porings
-rings are commutative rings whose factor rings modulo prime ideals are valuation rings. -rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of -rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of axiomatizability (in the sense of model theory). Partially ordered -rings (-porings) are introduced, and...
Sacks forcing collapses to
We shall prove that Sacks algebra is nowhere -distributive, which implies that Sacks forcing collapses to .
Safety- and liveness-properties in propositional temporal logic: characterizations and decidability
Saturated Boolean Algebras With Ultrafilters
Saturated Boolean algebras with ultrafilters.
Saturated models of incomplete theories.
Saturation and omitting types.
Schanuel Nullstellensatz for Zilber fields
We characterize the unsolvable exponential polynomials over the exponential fields introduced by Zilber, and deduce Picard's Little Theorem for such fields.
Scott sentences and a problem of Vaught for mono-uary algebras
Second order arithmetic and autonomous computability.
Second order forcing, algebraically closed structures, and large cardinals