SPM Bulletin 28

TL;DR

The bulletin compiles recent research announcements and discussions on various topics in set theory, topology, and related areas, highlighting new results, open problems, and theoretical developments.

Contribution

It presents a collection of new research findings, conjectures, and open problems across multiple areas in mathematical logic and topology.

Findings

Introduction of ultrafilters with property (s)

Results on Banach's Fixed Point Theorem converse

Advances in stationary reflection and coloring theorems

Abstract

Contents: 1. Editor's note; 2. gamma-sets from a weak hypothesis; 3. Research announcements; 3.1. Ultrafilters with property (s); 3.2. On a converse to Banach's Fixed Point Theorem; 3.3. Analytic groups and pushing small sets apart 3.4. Club-guessing, stationary reflection, and coloring theorems; 3.5. More on the pressing down game; 3.6. A note on discrete sets; 3.7. Antidiamond principles and topological applications; 3.8. Partitions and indivisibility properties of countable dimensional vector spaces; 3.9. Group-valued continuous functions with the topology of pointwise convergence; 3.10. Stationary and convergent strategies in Choquet games; 3.11. Linear sigma-additivity and some applications; 4. Unsolved problems from earlier issues.