This paper presents an extension of a proof system for encoding generic judgments, the logic FOλ∆∇ of Miller and Tiu, with an induction principle. The logic FOλ∆∇ is itself an extension of intuitionistic logic with fixed points and a “generic quantifier”, ∇, which is used to reason about the dynamics of bindings in object systems encoded in the logic. A previous attempt to extend FOλ∆∇ with an ...

Fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models. With Zadeh’s extension principle, one can obtain a fuzzy extension of any objective function. Computing expensive multivariate functions of fuzzy numbers, however, often poses a difficult problem due to non-applicability of common fuzzy arithmetic algorithms, severe overestimation, or very high computat...

We prove that a nonstandard extension of arithmetic is eeectively conservative over Peano arithmetic by using an internal version of a deenable ultrapower. By the same method we show that a certain extension of the nonstandard theory with a saturation principle has the same proof-theoretic strength as second order arithmetic, where comprehension is restricted to arithmetical formulas.

We extend the “Extension after Restriction Principle” for symplectic embeddings of bounded starlike domains to a large class of symplectic embeddings of unbounded starlike domains.

— Let P (t) ∈ Q[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of Q containing the roots of P (t). Let NK/Q(x) be a full norm form for the extension K/Q. We show that the variety P (t) = NK/Q(x) 6= 0 satisfies the Hasse principle and weak approximation. The proof uses analytic methods.

We propose the extension of the spectral action principle to fermions and show that the neutrino mass terms appear then naturally as nextorder corrections.

Extensions (modifications) of the Heisenberg Uncertainty principle are derived within the framework of the theory of Special Scale-Relativity proposed by Nottale. In particular , generalizations of the Stringy Uncertainty Principle are obtained where the size of the strings is bounded by the Planck scale and the size of the Universe. Based on the fractal structures inherent with two dimensional...

Extensions (modiications) of the Heisenberg Uncertainty principle are derived within the framework of the theory of Special Scale-Relativity proposed by Nottale. In particular , generalizations of the Stringy Uncertainty Principle are obtained where the size of the strings is bounded by the Planck scale and the size of the Universe. Based on the fractal structures inherent with two dimensional ...

Extensions (modi cations) of the Heisenberg Uncertainty principle are derived within the framework of the theory of Special Scale-Relativity proposed by Nottale. In particular, generalizations of the Stringy Uncertainty Principle are obtained where the size of the strings is bounded by the Planck scale and the size of the Universe. Based on the fractal structures inherent with two dimensional Q...

In this paper a duality principle is formulated for statements about skew field extensions of finite (left or right) degree. A proof for this duality principle is given by constructing for every extension L/K of finite degree a dual extension LJK, . These dual extensions are constructed by embedding a given L/K in an inner Galois extension N/K. The Appendix shows that such an embedding can alwa...