SPM Bulletin 27

TL;DR

This bulletin compiles diverse research announcements in topology, set theory, and analysis, highlighting recent advances, open problems, and new results across multiple mathematical disciplines.

Contribution

It provides a comprehensive overview of recent developments and open questions in various areas of mathematical research, serving as a valuable resource for researchers.

Findings

New constructions of pseudocompact group topologies

Results on partition relations below density 2

Advances in combinatorial and model-theoretical principles

Abstract

Contents: 1. Editor's note 2. Research announcements 2.1. Pseudocompact group topologies with no infinite compact subsets 2.2. Selective coideals on (FIN[1]k) 2.3. Entire functions mapping uncountable dense sets of reals onto each other monotonically 2.4. Effective refining of Borel coverings 2.5. Symmetry and colorings: Some results and open problems 2.6. Many partition relations below density 2.7. Lindelof indestructibility, topological games and selection principles 2.8. Locally precompact groups: (Local) realcompactness and connectedness 2.9. The group Aut is Roelcke precompact 2.10. An infinite combinatorial statement with a poset parameter 2.11. The Schur `1 Theorem for fifilters 2.12. On uniform asymptotic upper density in locally compact abelian groups 2.13. A c0-saturated Banach space with no long unconditional basic sequences 2.14. Zero subspaces of polynomials on `1(2.15. MAD Families and SANE Player 2.16. On the consistency of d_k > cov_k(M) 2.17. o-Boundedness of free topological groups 2.18. Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. V 2.19. Menger subsets of the Sorgenfrey line 2.20. Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. VI 3. Unsolved problems from earlier issues