We prove that if y′′ = f(y, y′, t, α, β, . . .) is a generic Painlevé equation from among the classes II to V , and if y1, . . . , yn are distinct solutions, then tr.deg (C(t)(y1, y′ 1, . . . , yn, y′ n)/C(t)) = 2n. (This was proved by Nishioka for the single equation PI .) For generic Painlevé VI, we have a slightly weaker result: ω-categoricity (in the sense of model theory) of the solution s...

In addition to those who served in the Union Defence Forces there were many South Africans who were serving in the British or Commonwealth forces or who joined up where they were on the outbreak of war. Since their service records are not readily available it is not possible to compile a definitive article on this topic at this stage. Even the records of our own personnel seconded to the Britis...

The independence problems for functionalism stem from the worry that functional properties that are defined in terms of their causes and effects are not sufficiently independent of those purported causes and effects. I distinguish three different ways the independence problems can be filled out—in terms of necessary connections, conceptual connections and vacuous explanations. I argue that none...

We examine fields in which model theoretic algebraic closure coincides with relative field theoretic algebraic closure. These are perfect fields with nice model theoretic behaviour. For example, they are exactly the fields in which algebraic independence is an abstract independence relation in the sense of Kim and Pillay. Classes of examples are perfect PAC fields, model complete large fields a...

A recent wave of economic research has studied the transformation of China from a poor country in the 1970s to a middle-income economy today. Based on this literature, we discuss the factors driving China’s development process. We provide a historical account of China’s rise, fall, and resurgence.We then discuss the stylized facts associated with China’s growth process and review a comprehensiv...