Related papers: Weyl and intuitionistic infinitesimals
In default reasoning, usually not all possible ways of resolving conflicts between default rules are acceptable. Criteria expressing acceptable ways of resolving the conflicts may be hardwired in the inference mechanism, for example…
Currently the two popular ways to practice Robinson's nonstandard analysis are the model-theoretic approach and the axiomatic/syntactic approach. It is sometimes claimed that the internal axiomatic approach is unable to handle constructions…
We find the Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the…
The intuitive reasoning of physicists in conditions of uncertainty is closer to the Bayesian approach than to the frequentist ideas taught at University and which are considered the reference framework for handling statistical problems. The…
We provide a novel perspective on "regularity" as a property of representations of the Weyl algebra. We first critique a proposal by Halvorson [2004, "Complementarity of representations in quantum mechanics", Studies in History and…
In the present paper and as an application of Roth's theorem concerning the rational approximation of algebraic numbers, we give a sufficient condition that will assure us that a sum, product and quotient of some series of positive rational…
In this paper we considered the extension of the First-order Logic (FOL) by Bealer's intensional abstraction operator. Contemporary use of the term 'intension' derives from the traditional logical Frege-Russell's doctrine that an idea…
In his remarkable paper Formalism64, Robinson defends his philsophocal position as follows: (i) Any mention of infinite totalities is literally meaningless. (ii) We should act as if infinite totalities really existed. Being the originator…
In the first part of the paper we propose a different viewpoint on the theory of higher Airy structures (or Airy ideals) which may shed light on its origin. We define Airy ideals in the $\hbar$-adic completion of the Rees Weyl algebra, and…
We present some similarities between Leibnizian and Robinsonian calculi, and address some objections raised by historians. The comparison with NSA facilitates our appreciation of some Leibnizian procedures that may otherwise seem obscure.…
Two types of approximation to the paradoxical Russell Set are presented, one approximating it from below, one from above. It is shown that any lower approximation gives rise to a better approximation containing it, and that any upper…
This work explores Everett John Nelson's connexive logic, outlined in his PhD thesis and partially summarized in his 1930 paper \emph{Intensional Relations}, which is obtained by extending the system $\mathsf{NL}$ (reconstructed by E. Mares…
The Basic Universal Deformation Formula is proven and applied to show that Weyl algebras, which encode Heisenberg's uncertainty principle, are effective deformations of polynomial rings, and that uncertainty is necessary for stability.…
Let R be the set of isomorphism classes of ideals in the Weyl algebra $A=A_{1}$, and let C be the set of isomorphism classes of triples (V; X, Y), where V is a finite-dimensional (complex) vector space, and X, Y are endomorphisms of V such…
During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to…
The Weyl principle is extended from the Riemannian to the pseudo-Riemannian setting, and subsequently to manifolds equipped with generic symmetric $(0,2)$-tensors. More precisely, we construct a family of generalized curvature measures…
We outline an abstract approach to the pseudo-differential Weyl calculus for operators in function spaces in infinitely many variables. Our earlier approach to the Weyl calculus for Lie group representations is extended to the case of…
Let W be a Weyl group. We define a class of irreducible representations of W that we call antispecial. They are in bijection with the constructible representations of W. We define an oriented graph structure on the set of antispecial…
To describe the representation theory of the quantum Weyl algebra at an $l$th primitive root $\gamma$ of unity, Boyette, Leyk, Plunkett, Sipe, and Talley found all nonsingular irreducible matrix solutions to the equation $yx-\gamma xy=1$,…
We present a new link between the Invariant Theory of infinitesimal singular Riemannian foliations and Jordan algebras. This, together with an inhomogeneous version of Weyl's First Fundamental Theorems, provides a characterization of the…