Forcing closed unbounded subsets of ℵω1+1

2. Trees and subsets of ℵω1+1..................... 7 3. Split squares........................... 11 4. Adding a club subset to ST adds a branch to T............ 15 5. Adding a club subset to ST when T has a branch........... 1

Forcing closed unbounded subsets of ℵω1+1

2. Trees and subsets of ℵω1+1..................... 8 3. Split squares........................... 11 4. Adding a club subset to ST adds a branch to T............ 16 5. Adding a club subset to ST when T has a branch........... 1