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.