Abstract
Measuring says that for every sequence $(C_\delta)_{\delta<\omega_1}$ with each $C_\delta$ being a closed subset of $\delta$ there is a club $C\subseteq\omega_1$ such that for every $\delta\in C$,a tail of $C\cap\delta$ is either contained in or disjoint from $C_\delta$. We answer a question of Justin Moore by building a forcing extension satisfying measuring together with $2^{\aleph_0}>\aleph_2$. The construction works over any model of ZFC + CH and can be described as a finite support forcing iteration with systems of countable models as side conditions and with symmetry constraints imposed on its initial segments. One interesting feature of this iteration is that it adds dominating functions $f:\omega_1\longrightarrow\omega_1$ mod. countable at each of its stages.
Original language  English 

Pages (fromto)  10661079 
Number of pages  14 
Journal  Journal of Symbolic Logic 
Volume  82 
Issue number  3 
Early online date  8 Sep 2017 
DOIs  
Publication status  Published  Sep 2017 
Keywords
 Measuring
 large continuum
 iterated forcing with symmetric systems of models as side conditions
Profiles

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