Géométrie asymptotique des courbes algébriques
Giving lectures on nonstandard analysis. (Lire l'analyse non standard.)
Harmonic Analysis and nonstandard Brownian Motion in the plane.
Herbrand consistency and bounded arithmetic
We prove that the Gödel incompleteness theorem holds for a weak arithmetic Tₘ = IΔ₀ + Ωₘ, for m ≥ 2, in the form Tₘ ⊬ HCons(Tₘ), where HCons(Tₘ) is an arithmetic formula expressing the consistency of Tₘ with respect to the Herbrand notion of provability. Moreover, we prove , where is HCons relativised to the definable cut Iₘ of (m-2)-times iterated logarithms. The proof is model-theoretic. We also prove a certain non-conservation result for Tₘ.
Holonomie et cycle évanouissant
On démontre que l’holonomie est non triviale au voisinage d’un cycle évanouissant au moyen d’un critère d’Imanishi et on donne une démonstration non standard de ce dernier.
Homology theory in the alternative set theory I. Algebraic preliminaries
The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative -group), is introduced. Commutative -groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special...
Homomorphismes discontinus des algèbres de Banach commutatives séparables
Hyperdefinite stochastic integration I: The nonstandard theory.
Hyperdefinite stochastic integration II: Comparision with the standard theory.
Hyperdefinite stochastic integration III: Hyperdefinite representations of standard martingales.
Hyperfinite and standard unifications for physical theories.
Indicators, recursive saturation and expandability
Indiscernibles and dimensional compactness
This is a contribution to the theory of topological vector spaces within the framework of the alternative set theory. Using indiscernibles we will show that every infinite set in a biequivalence vector space , such that for distinct , contains an infinite independent subset. Consequently, a class is dimensionally compact iff the -equivalence is compact on . This solves a problem from the paper [NPZ 1992] by J. Náter, P. Pulmann and the second author.
Indiscernibles in the alternative set theory
Initial segments and isomorphic images of nonstandard models of arithmetic
Internally standard set theories
Intrinsic Stochastic Processes.
Invariant subspaces for polynomially compact almost superdiagonal operators on .
K vývoju matematiky infinitezimálna a nekonečna
Kneser’s theorem for upper Banach density
Suppose is a set of non-negative integers with upper Banach density (see definition below) and the upper Banach density of is less than . We characterize the structure of by showing the following: There is a positive integer and a set , which is the union of arithmetic sequences [We call a set of the form an arithmetic sequence of difference and call a set of the form an arithmetic progression of difference . So an arithmetic progression is finite and an arithmetic sequence...