We present a new non-Archimedean realization of the Fock representation q-oscillator algebras where creation and annihilation operators act on complex-valued functions, which are defined local field arbitrary characteristic, for instance, p-adic numbers. This implies that many quantum models constructed using models, in particular, models. In this framework, we select q-deformation Heisenberg u...

Let M be a number field, and WM a set of its non-Archimedean primes. Then let OM,WM = {x ∈M | ordt x ≥ 0, ∀t 6∈ WM}. Let {p1, . . . , pr} be a finite set of prime numbers. Let Finf be the field generated by all the pji -th roots of unity as j → ∞ and i = 1, . . . , r. Let Kinf be the largest totally real subfield of Finf . Then for any ε > 0, there exist a number field M ⊂ Kinf , and a set WM o...

To allow conditioning on counterfactual events, zero probabilities can be replaced by infinitesimal probabilities that range over a non-Archimedean ordered field. This paper considers a suitable minimal field that is a complete metric space. Axioms similar to those in Anscombe and Aumann (1963) and in Blume, Brandenburger and Dekel (1991) are used to characterize preferences which: (i) reveal u...