SPM Bulletin 25

TL;DR

This bulletin compiles diverse recent research in set theory, topology, and combinatorics, covering principles related to ultrafilters, topological group properties, Ramsey theory, and forcing, among others.

Contribution

It provides a comprehensive overview of new results and methods across multiple areas in mathematical logic and topology, highlighting advances in ultrafilter regularity, topological dynamics, and combinatorial principles.

Findings

New principles related to ultrafilter regularity and compactness

Results on Frechet-Urysohn fans in free topological groups

Advances in Ramsey theory and topological dynamics

Abstract

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 Hausdorff's 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 Shelah's Strong Hypothesis; 24. Superfilters, Ramsey theory, and van der Waerden's Theorem.