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Authors
Boaz Tsaban
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Contents: 1. Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces, I; 2. Frechet-Urysohn fans in free topological groups; 3. Packing index of subsets in Polish groups; 4. Symmetric monochromatic subsets in colorings of the Lobachevsky plane; 5. Structural Ramsey theory of metric spaces and topological dynamics of isometry groups; 6. Distinguishing Number of Countable Homogeneous Relational Structures; 7. Indestructible colourings and rainbow Ramsey theorems; 8. Products of Borel subgroups; 9. Selection theorems and treeability; 10. Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces, IV; 11. A property of Cp[0, 1]; 12. A Dedekind Finite Borel Set; 13. Aronszajn Compacta; 14. A strong antidiamond principle compatible with CH; 15. On the strength of Hausdorffs gap condition; 16. Nonhomogeneous analytic families of trees; 17. Reasonable non-Radon-Nikodym ideals; 18. Continuity and related forcing; 19. An exact Ramsey principle for block sequences; 20. Baire reflection; 21. Tukey classes of ultrafilters on; 22. Countably determined compact abelian groups; 23. A topological reflection principle equivalent to Shelahs Strong Hypothesis; 24. Superfilters, Ramsey theory, and van der Waerdens Theorem.
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A surprising number of new results in core SPM in the last quarter of 2007, and some other beautiful fundamental results are announced.
1. A Wikipedia entry on topological games 2. On a fragment of the universal Baire property for sigma^1_2 sets 3. The coarse classification of homogeneous ultra-metric spaces 4. Ramsey-like embeddings 5. Proper and piecewise proper families of reals 6. Measures and their random reals 7. Obtainable Sizes of Topologies on Finite Sets 8. Spaces of R-places of rational function fields 9. All properties in the Scheepers Diagram are linearly-sigma-additive.
Contents: 2. Invited contribution: Ultrafilters and small sets 3. Research announcements 3.1. Inverse Systems and I-Favorable Spaces 3.2. Combinatorial and hybrid principles for sigma-directed families of countable sets modulo finite 3.3. A dichotomy characterizing analytic digraphs of uncountable Borel chromatic number in any dimension 3.4. A dichotomy characterizing analytic digraphs of uncountable Borel chromatic number in any dimension 3.5. Large continuum, oracles 3.6. Borel hierarchies in infinite products of Polish spaces 3.7. A game for the Borel functions 3.8. On some problems in general topology 4. Problem of the Issue
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.
With the approaching TOPOSYM16 (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 good number of the contributed lecture speakers, made substantial contributions to this topic in their career. For some of these, SPs constitute the main topic of research in the last few years. This is in accordance with the continuous progress on the topic, some of which reported in this bulletin.
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