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 club--sequence $\la C_\d\mid \d\in \k^+\cap\cf(\k)\ra$ 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 |
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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 | 5-27 |
Number of pages | 23 |
Volume | Tributes 23 |
ISBN (Electronic) | 978-1848901308 |
ISBN (Print) | 1848901305 |
Publication status | Published - 2014 |
Profiles
-
David Aspero
- School of Engineering, Mathematics and Physics - Associate Professor in Pure Mathematics
- Algebra, Number Theory, Logic, and Representations (ANTLR) - Member
Person: Research Group Member, Academic, Teaching & Research