Abstract
I answer a question of Shelah by showing that if $\k$ is a regular cardinal such that $2^{{<}\k}=\k$, then there is a ${<}\k$closed partial order preserving cofinalities and forcing that for every clubsequence $\la C_\d\mid \d\in \k^+\cap\cf(\k)\ra$ with $\ot(C_\d)=\k$ for all $\d$ there is a club $D\sub\k^+$ such that $\{\a<\k\mid \{C_\d(\a+1), C_\d(\a+2)\}\sub D\}$ is bounded for every $\d$. This forcing is built as an iteration with ${<}\k$supports and with symmetric systems of submodels as side conditions.
Original language  English 

Title of host publication  Infinity, computability, and metamathematics: Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch 
Editors  Stefan Geschke, Benedikt Loewe, Philipp Schlicht 
Place of Publication  London 
Publisher  College Publications 
Pages  527 
Number of pages  23 
Volume  Tributes 23 
ISBN (Electronic)  9781848901308 
ISBN (Print)  1848901305 
Publication status  Published  2014 
Profiles

David Aspero
 School of Mathematics  Associate Professor in Pure Mathematics
 Logic  Member
Person: Research Group Member, Academic, Teaching & Research