Abstract We show that there is no theory minimal with respect to interpretability among recursively enumerable essentially undecidable theories.

During the first three days of September, 1997, I had the privilege of giving a series of five lectures at the beginning of the “School on Algebraic K-Theory and Applications” at the International Center for Theoretical Physics in Trieste. What follows are the written notes of my lectures, essentially in the form distributed to the audience. I am especially grateful to Professor Adremi Kuku for...

In this paper we investigate families of quadratic twists of elliptic curves. Addressing a speculation of Ono, we identify a large class of elliptic curves for which the parities of the “algebraic parts” of the central values L(E/Q, 1), as d varies, have essentially the same multiplicative structure as the coefficients ad of L(E/Q, s). We achieve this by controlling the 2-Selmer rank (à la Mazu...

| It is well known that a convolutional code is essentially a linear system deened over a nite eld. In this paper we elaborate on this connection. We will deene convolutional codes as the dual of a complete linear behavior in the sense of Willems. Using ideas from systems theory we describe a set of generalized rst order descriptions for convolutional codes. As an application of these ideas, we...

Let K be an algebraic number field, and π = ⊗πv an irreducible, automorphic, cuspidal representation of GLm(AK) with analytic conductor C(π). The theorem on analytic strong multiplicity one established in this note states, essentially, that there exists a positive constant c depending on ε > 0,m, and K only, such that π can be decided completely by its local components πv with norm N(v) < c · C...

The idea of the mini-course is to review the formulation of quantum theories from an advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions due to von Neumann, discussing some fundamental ideas, mathematical tools and theorems in particular related to the representation of physical symmetries (Gleason, Wigner-Kadison, Stone Stone-von Neumann, Garding, Nelso...

Inspiration: Simple noncompact connected Lie groups — Irreducible symmetric spaces of noncompact type (E.Cartan et al). Here there is an essentially 1-1 correspondence between algebraic objects (a Lie group of a certain type) and geometric objects (certain symmetric spaces). Namely, given a Lie group G on constructs a symmetric space X = G/K (K is a maximal compact subgroup of G) and, conversel...

Preframes (directed complete posets with finite meets that distribute over the directed joins) are the algebras for an infinitary essentially algebraic theory, and can be presented by generators and relations. This result is combined with a general argument concerning categories of commutative monoids to give a very short proof of the localic Tychonoff Theorem. It is also shown how frames can b...