We provide a general preservation theorem for preserving selective independent families along countable support iterations. The gives framework number of results in the literature concerning models which independence i is strictly below c, including iterations Sacks forcing, Miller partition h-perfect tree forcings, coding with perfect trees. Moreover, applying theorem, we show that i=ℵ1 Lite m...

The influx of Polish workers into the UK requires a renewal of migration theories and presents important empirical puzzles. Both problems stem from the specificity of this migration wave, which does not correspond to classical models. The inadequacy of classical migration theories is demonstrated by the inaccuracy of forecasts from before 2004. The ‘optimistic’ forecasts (e.g. Boeri and Brücker...

Robert Peters,1,* Shintaro Hoshino,2 Norio Kawakami,1 Junya Otsuki,2,3 and Yoshio Kuramoto2 1Department of Physics, Kyoto University, Kyoto 606-8502, Japan 2Department of Physics, Tohoku University, Sendai 980-8578, Japan 3Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany (Received 21 February 2013;...

The combinatorial properties of Cohen forcing imply the existence of a countably closed, א2-c.c. forcing notion P which adds a C(ω2)-name Q for a σ-centered poset such that forcing with Q over V P×C(ω2) adds a real not split by V C(ω2) ∩ [ω] and preserves that all subfamilies of size ω1 of the Cohen reals are unbounded.