相关论文: SPM Bulletin 22

This is the 34th issue of this bulletin, dedicated to selection principles in mathematics. Announcements include, among other things, a call for papers for the Topology and its Applications special issue on selection principles, and the…

Never has an issue of the SPM Bulletin contained as much interesting information as this issue does. In addition to the interesting research announcements, this issue contains announcements of solutions for three open problems, one of which…

In addition to research announcements, this issue features a call for papers to a Topology and its Applications special issue, and an intriguing open problem.

A unique analytic continuation result is proved for solutions of a relatively general class of difference equations, using techniques of generalized Borel summability. This continuation allows for Painlev\'e property methods to be extended…

Dimensional types of metric scattered spaces are investigated. Revised proofs of Mazurkiewicz-Sierpi\'nski and Knaster-Urbanik theorems are presented. Embeddable properties of countable metric spaces are generalized onto uncountable metric…

This is the 30th issue of this bulletin, dedicated to mathematical selection principles and related areas. Now in a concise format.

In this issue we announce a fascinating series of works on the comparison of various types of convergence of sequences of functions. Some of these properties are provably related to some of the properties which were introduced in the…

With the approaching TOPOSYM'16 (http://www.toposym.cz/programme.php), it is a pleasure to see selection principles gain increasing attention and becoming a standard part of topology and set theory. At least eight of the 28 speakers, and a…

This is a translation into English of a paper written in French, published in Tatra Mountains Mathematical Publications, {L'ultrafiltre, un outil incomparable}, Tatra Mt. Math. Publ. {\bf 31} (2005), 131-176.It was also posted as…

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…

The survey covers several topics related to the asymptotic structure of various combinatorial and analytic objects such as the path spaces in graded graphs (Bratteli diagrams), invariant measures with respect to countable groups, etc. The…

We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…

These notes started to educate ourselves and to collect some background for our future work, with the hope that perhaps they will be useful to others also. Many if not all results are more or less elementary or available in the literature,…

The classification of separable operator spaces and systems is commonly believed to be intractable. We analyze this belief from the point of view of Borel complexity theory. On one hand we confirm that the classification problems for…

We study various combinatorial properties, and the implications between them, for filters generated by infinite-dimensional subspaces of a countable vector space. These properties are analogous to selectivity for ultrafilters on the natural…

This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…

Introduced is the notion of minimality for spectral representations of sum- and max-infinitely divisible processes and it is shown that the minimal spectral representation on a Borel space exists and is unique. This fact is used to show…

Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…

We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…

*** Note the comment above *** This is a special issue dedicated to the announcement of Shelah's recent solution of the Minimal Tower problem, one of the oldest and most important problems in infinite combinatorics which also motivated some…