Non-standard Extensions of Weak Presentations

Weak Presentations of Non-Finitely Generated Fields

Let K be a countable field. Then a weak presentation of K is an isomorphism of K onto a field whose elements are natural numbers, such that all the field operations are extendible to total recursive functions. Given a pair of two non-finitely generated countable fields contained in some overfield, we investigate under what circumstances the overfield has a weak presentation under which the give...

Weak Compactness of the Set of ε-Extensions

Non-supersymmetric Extensions of the Standard Model

The title of my talk was chosen by the organizers and, while it was not their intention, they have defined my subject by what it is not. That leaves it for me to define what it is. So, in this talk “non-supersymmetric extensions of the standard model” means Dynamical Electroweak and Flavor Symmetry Breaking. To be specific, I will discuss aspects of technicolor 1 and extended technicolor . I be...

Standard and Non-standard Extensions of Lie algebras

We study the problem of quadruple extensions of simple Lie algebras. We find that, adding a new simple root α+4, it is not possible to have an extended Kac-Moody algebra described by a Dynkin-Kac diagram with simple links and no loops between the dots, while it is possible if α+4 is a Borcherds imaginary simple root. We also comment on the root lattices of these new algebras. The folding proced...

Extensions and presentations of transversal matroids

A transversal matroid M can be represented by a collection of sets, called a presentation of M , whose partial transversals are the independent sets of M . Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (single-element) transversal extensions of M and extensions of presentations of M . We ...