SPM Bulletin 21

TL;DR

The bulletin summarizes recent research in set theory and topology, including new results on coloring ordinals, Borel hierarchies, automorphisms of the Calkin algebra, and properties of topological spaces.

Contribution

It compiles recent advances and open problems in set theory and topology, highlighting new results and classifications in these areas.

Findings

Automorphisms of the Calkin algebra are all inner.

New classifications of CO spaces as continuous images of compact ordered spaces.

Results on coloring ordinals by reals and properties of Borel hierarchies.

Abstract

Contents: 1. Editor's note; 2. Personal impressions from the SPM07 meeting; 3. Research announcements; 3.1. Coloring ordinals by reals; 3.2. Long Borel Hierarchies; 3.3. Rothberger's property in finite powers; 3.4. Special subsets of the reals and tree forcing notions; 3.5. All automorphisms of the Calkin algebra are inner; 3.6. Continuous selections and sigma-spaces; 3.7. On the closure of the diagonal of a T1-space; 3.8. Splitting families and Noetherian type; 3.9. Even more simple cardinal invariants; 3.10. A classification of CO spaces which are continuous images of compact ordered spaces; 4. Problem of the Issue