A careful exposition of Zilber’s quasiminimal excellent classes and their categoricity is given, leading to two new results: the Lω1,ω(Q)definability assumption may be dropped, and each class is determined by its model of dimension א0. Boris Zilber developed quasiminimal excellent classes in [Zil05], in order to prove that his conjectural description of complex exponentiation was categorical. T...

"Ibn Sina (Arabic), also known as Avicenna (Latin) and Abu Ali Sina (Persian) was the most original and systematic Muslim philosopher. In this light he is mentioned by two celebrated historians of medieval western philosophy: A. Maurer states, "...his [ibn Sina's] philosophy is a highly personal achievement, ranking among the greatest in the history of philosophy;" and F. Copleston holds, "The ...

We show the properties of the blowup limits of Kähler Ricci flow solutions on Fano surfaces if Riemannian curvature is unbounded. As an application, on every toric Fano surface, we prove that Kähler Ricci flow converges to a Kähler Ricci soliton metric if the initial metric has toric symmetry. Therefore we give a new Ricci flow proof of existence of Kähler Ricci soliton metrics on toric surfaces.

A convenient method for defining a quasi-ordering, such as those used for proving termination of rewriting, is to choose the minimum of a set of quasi-orderings satisfying some desired traits. Unfortunately, a minimum in terms of set inclusion can be non-existent even when an intuitive “minimum” exists. We suggest an alternative to set inclusion, called “leanness”, show that leanness is a parti...

The combination of systemic lupus erythematosus, Sjogren's disease and severe diffuse glomerular nephritis has only rarely been reported. A 14-year-old girl is described with lupus nephritis in whom co-existent clinical and histological features of Sjogren's syndrome were found. These include bilateral parotid enlargement, xerostomia, increased serum amylase, reduced salivary secretion and lymp...

Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see [KMM] for introduction. In [SH2] it was conjectured that many of the interesting sets, associated with these varieties have something in common: they satisfy the ascending chain condition, which means that every increasing chain of elements terminates (in [SH2] it was called the upper se...

We establish the dichotomy property of [7] for multi-conclusion stable canonical rules of [1]. This yields an alternative proof of existence of bases of admissible rules for such well-known systems as IPC, S4, and K4.

In [I] we introduced the notion of transfer from a group over a local field to an associated endoscopic group, but did not prove its existence, nor do we do so in the present paper. Nonetheless we carry out what is probably an unavoidable step in any proof of existence: reduction to a local statement at the identity in the centralizer of a semisimple element, a favorite procedure of Harish Chan...

In this note, we prove the existence of Nash equilibria in infinite normal form games with compact sets of strategies and continuous payoffs by constructing Nash mappings. © 2010 Elsevier Ltd. All rights reserved.