H. G. Dales – författare

The nature of truth in mathematics is a problem which has exercised the minds of thinkers from at least the time of the ancient Greeks. The great advances in mathematics and philosophy in the twentieth centuryand in particular the proof of Gödel's theorem and the development of the notion of independence in mathematicshave led to new viewpoints on this question in our era. This book is the result of the interaction of a number of outstanding mathematicians and philosophersincluding Yurii Manin, Vaughan Jones, and Per Martin-Löfand their discussions of this problem. It provides an overview of the forefront of current thinking, and is a valuable introduction and reference for researchers in the area.

Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a naturally arising and deep question of analysis is independent of ZFC. It provides an accessible account of this result, and it includes a discussion, of Martin's Axiom and of the independence of CH.

This book gives a coherent account of the theory of Banach spaces and Banach lattices, using the spaces C_0(K)  of continuous functions on a locally compact  space K as the main example.  The study of C_0(K) has been an important area of functional analysis for many years.  It gives several new constructions, some involving Boolean rings, of this space as well as many results on the Stonean space of Boolean rings.  The book also discusses when Banach spaces of continuous functions are dual spaces and when they are bidual spaces.