Splitting families and forcing

AbstractAccording to [M.S. Kurilić, Cohen-stable families of subsets of the integers, J. Symbolic Logic 66 (1) (2001) 257–270], adding a Cohen real destroys a splitting family S on ω if and only if S is isomorphic to a splitting family on the set of rationals, Q, whose elements have nowhere dense boundaries. Consequently, |S|<cov(M) implies the Cohen-indestructibility of S. Using the methods developed in [J. Brendle, S. Yatabe, Forcing indestructibility of MAD families, Ann. Pure Appl. Logic 132 (2–3) (2005) 271–312] the stability of splitting families in several forcing extensions is characterized in a similar way (roughly speaking, destructible families have members with ‘small generalized boundaries’ in the space of the reals). Also, it is proved that a splitting family is preserved by the Sacks (respectively: Miller, Laver) forcing if and only if it is preserved by some forcing which adds a new (respectively: an unbounded, a dominating) real. The corresponding hierarchy of splitting families is investigated

Civil Defence Policy in Cold War Britain, 1945-68

PhDThis thesis investigates how successive postwar British Governments formulated a civil defence policy aimed at ameliorating the effects of an enemy attack in the cold war. It shows that civil defence was a nuanced response to the prospect of nuclear attack framed in the changing political, economic and strategic contexts of cold war Britain. Beginning as a genuine life-saving measure, thermonuclear-era civil defence became an integral part of Britain's wider deterrence strategy. By locating civil defence within Britain's wider defence strategy, this thesis demonstrates the importance of civil defence as a key policy of the cold war state. It examines how civil defence policy was formulated, with studies of the effects of nuclear weapons and estimates of the consequences of an attack on British cities, and of the individual policies which were developed - especially evacuation, shelter, the voluntary Civil Defence Corps, and public information. It charts the changes in how civil defence was conceptualised and justified from the early cold war era to the period of detente after the Cuban Missile Crisis, details the responses to key cold war crises, and explains how economic retrenchment and developments in nuclear weapon technology, as well as detente, undermined civil defence policy and led to it being placed on a care-and-maintenance basis in 1968